Many references are linked directly to the journal article.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z – (Click on a letter)

Abe, K.: Sonine polynomial solution of the Boltzmann equation for relaxation of initially nonequilibrium distribution. Phys. Fluids 14, 492–498 (1971)
Abbott, D.: Overview: unsolved problems of noise and fluctuations. Chaos 11, 526–538 (2001)
Abolhassani, A.A.H., Matte, J.P.: Multi-temperature representation of electron velocity distribution functions. I. Fits to numerical results. Phys. Plasmas 19, 102103 (2012)
Abramowitz, M. and I. A. Stegun. 1964. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U.S. Government Printing Office.
Adcock, B., Hansen, A.C.: Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon. Appl. Comput. Harmon. Anal. 32, 357–388 (2012)
Adomaitis, R.A.: Spectral filtering for improved performance of collocation discretization methods. Comput. Chem. Eng. 25, 1621–1632 (2001)
Agarwal, R.K., Yun, K.-Y., Balakrishnan, R.: Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime. Phys. Fluids 13, 3061–3085 (2001)
Akhiezer, N. I.:  The Classical Moment Problem, Oliver and Boyd, London (1965)
Aleekseenko, A., Josyula, E.: Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space.
J. Comput.   Phys. 272, 170–188 (2014)
Alexandre, R.: A review of the Boltzmann equation with singular kernels. Kinet. Relat. Models 2, 551–646 (2009)
Al-Gwaiz, M.A.: Sturm-Liouville Theory and Its Applications. Springer, Berlin (2008)
Al-Khaled, K.: Numerical study of Fisher’s reaction-diffusion equation by the sinc collocation method, Comput. Appl. Math., 137, 245–255 (2001).
Almeida, P.G.C., Benilov, M.S., Naidis, G.V.: Calculation of ion mobilities by means of the twotemperature displaced-distribution theory. J. Phys. D: Appl. Phys. 35, 1577–1584 (2002)
Alp, Y. K. and Arikan, O: Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions. Digit. Signal Process., 22, 1010–1023 (2012)
Alterman, Z., Frankowski, K., Pekeris, C.L.: Eigenvalues and eigenfunctions of the linearized Boltzmann collision operator for a Maxwell gas and for a gas of rigid spheres. Astrophys. J. Suppl. 7, 291–331 (1962)
Alves, G.M., Kremer, G.M., Marques Jr, W., Soares, A.J.: A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes. J. Stat. Mech. 2011, P03014 (2011)
Anderson, D., Lisak, M., Andersson, F., Fülöp, T.: Slowing down dynamics of fast particles in
plasmas via the Fokker-Planck equation. Nucl. Sci. Eng. 146, 99–105 (2004)
Angula, C., et al.: A compilation of charged-particle induced thermonuclear reaction rates. Nucl. Phys. A 656, 3–183 (1999)
Amore, P.: A variational Sinc collocation method for strong-coupling problems, J. Phys. A: Math. Gen., 39, L349–L355 (2006)
Amore, P., Fernandez, F.M., Saenz, R.A., Salvo, K.: Collocation on uniform grids. J. Phys. A: Math. Theor. 42, 115302 (2009)
Andersen, H.C.: Derivation of hydrodynamic equations from the Boltzmann equation. In: Hochstim, A.E. (ed.) Kinetic Processes in Gasses and Plasmas, pp. 25–55. Elsevier, Holland (1969)
Andersen, K. and Shuler, K. E.: On the relaxation of a hard sphere Rayleigh and Lorentz gas, J. Chem. Phys., 40, 633–650 (1964).
Andersen, H.C., Oppenheim, I., Shuler, K.E., Weiss, G.H.: Exact condition for the preservation of a canonical distribution in Markovian relaxation process. J. Math. Phys. 5, 522–536 (1964)
Anna, J.M., Kubarych, K.J.: Watching solvent friction impede ultrafast barrier crossings: a direct test of Kramers theory. J. Chem. Phys. 133, 174506 (2010)
Archibald, R., Gelb, A.: Reducing the effects of noise in image reconstruction. J. Sci. Comput. 17, 167–180 (2002)
Asadchev, A. and M. S. Gordon, M. S.: Mixed-precision evaluation of two-electron integrals by Rys quadrature, Comp. Phys. Comm., 183, 1563–1567 (2012)
Asheim, A., Deano, A., Huybrechs, D., Wang, H.: A Gaussian quadrature rule for oscillatory integrals on a bounded interval. Discret. Contin. Dyn. Syst. 34, 883–901 (2014)
Atenzi, S., Meyer-Ter-Vehn, J.: The Physics of Inertial Fusion. Clarendon Press, Oxford (2004)
Atkinson, K.E., Shampine, L.F.: Algorithm 876: solving Fredholm integral equations of the second kind in MATLAB. ACM Trans. Math. Softw. 34, 21 (2008)
Avila, G. and T. Carrington Jr., T.: Nonproduct quadrature grids for solving the Schr¨odinger equation, J. Chem. Phys., 131, 174103 (2009).
Avila, G. and T. Carrington Jr., T.:Solving the Schr¨odinger equation using Smolyak interpolants, J. Chem. Phys. 139, 134114 (2009).
Azaez, M., El Fekih, H., Hesthaven, J.S.: Spectral and High Order Methods for Partial Differential Equations-ICOSAHOM. Springer, New York (2012)
Aziz, R.A., Slaman,M.J.: An examination of ab initio results for the helium potential energy curve. J. Chem. Phys. 94, 8047–8053 (1991)


Bachau, H., E. Cormier, P. Decleva, J. E. Hansen, and F. Martin, F: Application of B–Splines in atomic and molecular physics. Rep. Prog. Phys. 64, 1815–1942 (2001)
Bacic, Z., Light, J.C.: Theoretical methods for rovibrational states of floppy molecules. Annu. Rev. Phys. Chem. 40, 469–498 (1989)
Bacic, Z., Light, J.C.: Highly excited vibrational levels of floppy triatomic-molecules: a discrete variable representation—distributed Gaussian-basis approach. J. Chem. Phys. 85, 4594–4604 (1986)
Bagchi, B., Fleming, G.R., Oxtoby, D.W.: Theory of electronic relaxation in solution in the absence of an activation barrier. J. Chem. Phys. 78, 7375–7385 (1983)
Balakrishnan, N., Dalgarno, A.: Nitric oxide production in collisions of hot O(3P) atoms with N2. J. Geophys. Res. 108, 1065 (2003)
Balint-Kurti, G.G.: Wavepacket theory of photodissociation and reactive scattering. Adv. Chem. Phys. 128, 249–301 (2003)
Balint-Kurti, G.G.: Time-dependent and time-independent wavepacket approaches to reactive scattering and photodissociation dynamics. Int. Rev. Phys. Chem. 27, 507–539 (2008)
Balint-Kurti, G.G.: Wavepacket quantum dynamics. Theor. Chem. Acc. 127, 1–17 (2010)
Balint-Kurti, G.G., Pulay, P.: A new grid-based method for the direct computation of excited molecular vibrational-states: test application to formaldehyde. J. Mol. Struct. (Theochem) 341, 1–11 (1995)
Ball, J. S.: Half-range generalized Hermite polynomials and the related Gaussian quadratures, SIAM J. Numer. Anal., 40, 2311–2317 (2003)
Baltensperger, R., Trummer, M.A.: Spectral differencing with a twist. SIAM J. Sci. Comput. 24, 1465–1487 (2003)

Barkley, D.: Spiral meandering. In: Kapral, R., Showalter, K. (eds.) Chemical Waves and Patterns, pp. 163–189. Kluwer Academic, Norwell (1995)
Baltz, R. V.: Ein funktionensystem f¨ur zeit-und energieabh¨angige thermalisierungsprobleme, Atomk-ernergie (ATKE), 14-33, 179–181 (1969).
Bao, W., Li, H., Shen, J.: A generalized Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. J. Comput. Phys. 227, 9778–9793 (2008)
Baranger, C., Mouhot, C.: Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials. Rev. Mat. Iberoam. 3, 819–841 (2005)
Barrett, J., Demeio, L., Shizgal, B.: The Coulomb Milne problem. Phys. Rev. A 45, 3687–3699 (1992)
Bartlett, D.F., Corle, T.R.: The circular parallel plate capacitor: a numerical solution for the potential. J. Phys. A: Math. Gen. 18, 1337–1342 (1985)
Basu, B., Jasperse, J.R., Strickland, D.J., Daniel, R.E.: Transport-theoretic model for the electron proton-hydrogen atom aurora. J. Geophys. Res. 98, 21517–21532 (1993)
Baye, D.: Lagrange bases for the Fourier, generalized Fourier and Riccati-Bessel grids. J. Phys. B: Atom. Mol. Opt. Phys. 27, L187–L191 (1994)
Baye, D.: Constant-step Lagrange meshes for central potentials. J. Phys. B: At. Mol. Opt. Phys. 28, 4399–4412 (1995)
Baye, D.: Lagrange-mesh method for quantum-mechanical problems. Phys. Stat. Sol. B 243, 1095– 1109 (2006)
Baye, D., Vincke, M., Hesse, M.: Simple and accurate calculations on a Lagrange mesh of the hydrogen atom in a magnetic field. J. Phys. B: At. Mol. Opt. Phys. 41, 055005 (2008)
Baye, D., Vincke, V.: Lagrange meshes from nonclassical orthogonal polynomials. Phys. Rev. E 59, 7195–7199 (1999)
Baye, D., Hesse, M., Vincke, M.: The unexplained accuracy of the Lagrange-mesh method. Phys. Rev. E 65, 026701 (2002)

Baye, D., Heenen, P.H.: Generalized meshes for quantum-mechanical problems. J. Phys. A: Math. Gen. 19, 2041–2059 (1986)
Beebe, N.H.F., Ball, J.S.: Algorithm 867:QUADLOG-Apackage of routines for generating Gauss—related quadrature for two classes of logarithmic weight functions. ACM. Trans. Math. Softw. 33, 1–30 (2007)
Becke, A.D.: Perspective: fifty years of density-functional theory in chemical physics. J. Chem. Phys. 140, 18A301 (2014)
Becke, A. D.; A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 88, 2547–2553 (1988).
Belai, O. V., Schwartz, O.Y., Shapiro, D. A.: Accuracy of one-dimensional collision integral in the rigid-sphere approximation. Phys. Rev. A 76, 012513 (2007)
Bellman, R.E., Kashef, B.G., Casti, J.: Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. 10, 40–52 (1972)
Berezhkovskii, A.M., Zitserman, V.Yu., Polimenob, A.: Numerical test of Kramers reaction rate theory in two dimensions. J. Chem. Phys. 105, 6342–6357 (1996)
Berman, P.R., Haverkort, J.E.M.,Woerdman, J.P.: Collision kernels and transport coefficients. Phys. Rev. A 34, 4647–4656 (1986)
Bernstein, R.B.: Quantum effects in elastic molecular scattering. Adv. Chem. Phys. 10, 75–134 (1966)
Bernstein, M., Brown, L.S.: Supersymmetry and the bistable Fokker-Planck equation. Phys. Rev. Lett. 52, 1933–1935 (1984)
Bertulani, C.A., Fuqua, J., Hussein, M.S.: Big bang nucleosynthesis and non-Maxwellian distribution. Astrophys. J. 767(63), 1–11 (2013)
Bhattacharyya, B.: Bounds on the ground state energy: application of the variational principle. Am. J. Phys. 77, 44–47 (2009)
Bhatnagar, P.L., Gross, E.P., Krook, M.:Amodel for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954)
Bi, C., Chakraborty, B.: Rheology of granular materials: dynamics in a stress landscape. Philos. Trans. R. Soc. A 367, 5073–5090 (2009)
Bicout, D.J., Szabo, A.: Entropic barriers, transition states, funnels, and exponential protein folding kinetics: a simple model. Protein Sci. 9, 452–465 (2000)
Bicout, D.J., Berezhkovskii, A.M., Szabo, A.: Irreversible bimolecular reactions of Langevin particles. J. Chem. Phys. 114, 2293–2303 (2001)
Binney, J., Tremaine, S.: Galactic Dynamics, 2nd edn. Princeton University Press, New Jersey (2008)
Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon, Oxford (1994)
Birdsall, C.K., Langdon, A.B.: Plasma Physics via Computer Simulation. McGraw-Hill, New York (1984)
Biró, T.S., Jakovác, A.: Power-law tails from multiplicative noise. Phys. Rev. Lett. 94, 132302 (2005)
Blackledge, J.M.: Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications. Woodhead, Cambridge (2006)
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)
Blackmore, R.S.:  Theoretical studies in stochastic processes. PhD thesis, UBC (1985)
Blackmore, R., Shizgal, B.: Discrete ordinate method of solution of Fokker-Planck equations with nonlinear coefficients. Phys. Rev. A 31, 1855–1868 (1985)
Blackmore, R., Shizgal, B.: A solution of Kramers equation for the isomerization of n-butane in CCl4. J. Chem. Phys. 83, 2934–2941 (1985b)
Blackmore, R., Weinert, U., Shizgal, B.: Discrete ordinate solution of a Fokker-Planck equation in laser physics. Trans. Theory Stat. Phys. 15, 181–210 (1986)
Blaise, P., Kalmykov, Y.P., Velcescu, A.A.: Extended diffusion in a double well potential: transition from classical to quantum regime. J. Chem. Phys. 137, 094105 (2012)
Blinnikov, S., Moessner, R.: Expansions for nearly Gaussian distributions. Astron. Astrophys. Suppl. Ser. 130, 193–205 (1998)
Bobylev, A.V.: A class of invariant solutions of the Boltzmann equation. Dokl. Akad. Nauk SSSR 231, 571–574 (1976)
Bobylev, A.V.: Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas. Theor. Math. Phys. 60, 820–841 (1984)
Bobylev, A.V., Cercignani, C.: On the rate of entropy production for the Boltzmann equation. J. Stat. Phys. 94, 603–618 (1999)
Bobylev, A.V., Mossberg, E.: On some properties of linear and linearized Boltzmann collision operators for hard spheres. Kinet. Relat. Models 1, 521–555 (2008)
Boley, D., Golub, G.H.: A survey of matrix inverse eigenvalue problems. Inverse Probl. 3, 595–622 (1987)
Bonazzola, S., Gourgoulhon, E., Marck, J.-A.: Spectral methods in general relativistic astrophysics. J. Comput. Appl. Math. 109, 433–473 (1999)
Bonifacio, R., Gronchi, M., Lugiato, L.A.: Photon statistics of a bistable absorber. Phys. Rev. A 18, 2266–2279 (1978)
Bordoni, A., Manini, N.: An optimized algebraic basis for molecular potentials. J. Phys. Chem. A 111, 12564–12569 (2007)
Bornemann, F., Laurie, D., Wagon, S., Waldvogel, J.: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. SIAM, Philadelphia (2004)
Borromeo, M., Marchesoni, F.: Asymmetric probability densities in symmetrically modulated bistable devices. Phys. Rev. E 71, 031105 (2005)
Bosch, H.S., Hale, G.M.: Improved formulas for fusion cross sections and thermal reactivities. Nucl. Fusion 32, 611–631 (1992)
Bovino, S., Zhang, P., Kharchenko, V., Dalgarno, A.: Trapping hydrogen atoms from a Neon-gas matrix: a theoretical simulation. J. Chem. Phys. 131, 054302 (2009)
Bovino, S., Zhang, P., Kharchenko, V., Dalgarno, A.: Relaxation of energetic S(1D) atoms in Xe gas: comparison of ab initio calculations with experimental data. J. Chem. Phys. 135, 024304 (2011)
Boyd, J.P.: The optimization of convergence for Chebyshev polynomial methods in an unbounded domain. J. Comput. Phys. 45, 43–79 (1982)
Boyd, J.P.: Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite domains. J. Sci. Comput. 2, 99–109 (1987)
Boyd, J.P.: A fast algorithm for Chebyshev, Fourier, and Sine interpolation onto an irregular grid. J. Comput. Phys. 103, 243–257 (1992)
Boyd, J.P.: A numerical comparison of seven grids for polynomial interpolation on the interval. Comput. Math. Appl. 38, 35–50 (1999)
Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Dover, New York (2001)
Boyd, J.P.: A spectrally accurate quadrature for resolving the logarithmic endpoint singularities of the Chandrasekhar H-function. JQRST 94, 467–475 (2005)
Boyd, J.P.: Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval. Comput. Math. Appl. 60, 3108–3122 (2010)
Boyd, J.P., Ong, J.R.: Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions, Part I: single-interval schemes. Commun. Comput. Phys. 5, 484–497 (2009)
Boyd, J.P., Ong, J.R.: Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions, part two: multi-interval polynomial schemes and multidomain Chebyshev interpolation. Appl. Numer. Math. 61, 460–472 (2011)
Boyd, J.P., Wang, L.: Truncated Gaussian RBF differences are always inferior to finite-differences of the same stencil width. Commun. Comput. Phys. 5, 42–60 (2009)
Boyd, J.P., Rangan, C., Bucksbaum, P.H.: Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions. J. Comput. Phys. 188, 56–74 (2003)
Boyd, T.J.M., Sanderson, J.S.: The Physics of Plasmas. Cambridge University Press, Cambridge (2003)
Braun, M., Sofianos, S.A., Papageorgiou, D.G., Lagaris, I.E.: An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid. J. Comput. Phys. 126, 315–327 (1996)
Brey, J.J., Casado, J.M., Morillo, M.: Combined effects of additive and multiplicative noise in a Fokker-Planck model. Z. Phys. B—Condens. Matter 66, 263–269 (1987)
Briggs, W.L., Henson, V.E.: The DFT; An Owners Manual for the Discrete Fourier Transform. SIAM, Philadelphia (1995)
Brinkmann, H.C.: Brownian motion in a field of force and the diffusion theory of chemical reactions. Physica A 22, 29–34 (1956)
Brinkman, R.T.: Departures from Jeans escape rate for H and He in the earth’s atmosphere. Planet. Space Sci. 18, 449–478 (1970)
Brown, J.W., Churchill, R.V.: Fourier Series and Boundary Value Problems. McGraw Hill, New Jersey (1993)
Brun, R.: Introduction to Reactive Gas Dynamics. Oxford University Press, Oxford (2009)
Buet, C., Dellacherie, S.: On the Chang Cooper scheme applied to a linear Fokker Planck equation. Commun. Math. Sci. 8, 1079–1090 (2010)
Buhmann, R.D.: Radial Basis Functions. Cambridge University Press, Cambridge (2004)
Burden, R.L., Faires, J.D.: Numerical Analysis, 9th edn. Brooks/Cole, Boston (2011)
Burke, P.G.: R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes. Springer, New York (2011)
Burke, K.: Perspective on density functional theory. J. Chem. Phys. 136, 150901 (2012)
Burke, P.G., Joachain, C.J.: Theory of Electron Atom Collisions Part 1: Potential Scattering. Springer, New York (1995)
Byrd, P.F., Galant, D.C.: Gauss Quadrature Rules Involving Some Nonclassical Weight Functions. Technical Report TN D-5785, NASA, 1–42 (1970)


Calabr`o, F. and A. C. Esposito. 2009. An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures, J. Comput. Appl. Math., 229, 120–128.
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, New York (1998)
Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, T. A.: Spectral Methods: Fundamentals in Single Domains, Springer, New York (2006).
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Mechanics. Springer, New York (2006)
Car, R., Parrinello, M.: Unified approach for molecular dynamics and density functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985)
Carlson, B. G.: Solution of the transport equation by SN approximation, Tech. Rep. LA-1981, Los Alamos Scientific Laboratory (1953).
Carlson, H.S.: A historical note on Gibb’s phenomenon in Fourier’s series and integrals. Bull. Am. Math. Soc. 31, 420–424 (1925)
Carsky, P. and Polasek, M;. Evaluation of molecular integrals in a mixed Gaussian and plane-wave basis by Rys quadrature, J. Comput. Phys., 143, 266–277 (1998)
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Fundamentals in Single Domains. Springer, New York (2006b)
Canto, L.F., Hussein, M.S.: Scattering Theory of Molecules. Atoms and Nuclei. Springer, NewYork (2013)
Cartling, B.: Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential. J. Chem. Phys. 87, 2638–2648 (1987)
Case, K.M., Zweifel, P.F.: Linear Transport Theory. Addison-Wesley, Reading (1967)
Cassam-Chenaï, P., Liévin, J.: Ab initio calculation of the rotational spectrum of methane vibrational ground state. J. Chem. Phys. 136, 174309 (2012)
Cassar, M.M., Drake, G.W.F.: High precision variational calculations for H+2 . J. Phys. B: At. Mol. Opt. Phys. 37, 2485–2492 (2004)
Cercignani, C.: A variational principle for boundary value problems in kinetic theory. J. Stat. Phys. 1, 297–311 (1969)
Cercignani, C.: The Boltzmann Equation and Its Applications. Springer, New York (1988)
Cha, S.-H.: Comprehensive survey on distance/similarity measures between probability density functions. Int. J Math. Models Methods Appl. Sci. 1, 300–307 (2007)
Chamberlain, J.W., Campbell, F.J.: Rate of evaporation of a non-Maxwellian atmosphere. Astrophys. J. 149, 687–705 (1967) (Chamberlain-Campbell-1967)
Chandrasekhar, S.: Principles of Stellar Dynamics. Dover, New York (1942)
Chandrasekhar, S.: On the radiative equilibrium of a stellar atmosphere II. Astrophys. J. 100, 76–86 (1944)
Chandrasekhar, S.: Brownian motion, dynamical friction, and stellar dynamics. Rev. Mod. Phys.  21, 383–388 (1949)
Chandrasekhar, S., Breen, F.H.: On the radiative equilibrium of a stellar atmosphere XIX. Astrophys. J. 105, 143–144 (1947) (Chandresekhar-Breen-1947)
Chandrasekhar, S.: Radiative Transfer, Dover, New York (1960)
Chapman, S., Cowling, T.G.: The Mathematical Theory of Nonuniform Gases. Cambridge University Press, Cambridge (1970)
Chang, J.C., Cooper, G.: A practical difference scheme for Fokker-Planck equations. J. Comput. Phys. 6, 1–16 (1970)
Chatfield, D.C., Truhlar, D.G., Schwenke, D.W.: Benchmark calculations for thermal reaction rates. I. Quantal scattering theory. J. Chem. Phys. 94, 2040–2044 (1991)
Chavanis, P.H.: Relaxation of a test particle in systems with long-range interactions: diffusion coefficient and dynamical friction. Eur. J. Phys. B 52, 61–82 (2006)
Chen, H., Shizgal, B.D.:A spectral solution of the Sturm-Liouville equation: comparison of classical and nonclassical basis sets. J. Comput. Appl. Math. 136, 17–35 (2001)
Chen, H.L., Su, Y.H., Shizgal, B.D.: A direct spectral collocation Poisson solver in polar and cylindrical coordinates. J. Comput. Phys. 160, 453–469 (2000)
Chen, H., Shizgal, B.D.: The quadrature discretization method (QDM) in the solution of the Schr¨odinger equation, J. Math. Chem., 24, 321–343 (1998)
Cheney, E.W.: Introduction to Approximation Theory. McGraw-Hill, New York (1966)
Cheney, W., Kincaid, D.: Numerical Methods and Computing, 6th edn. Brooks/Coll Publishing Company, California (2008)
Chien, S.-H., Gill, P.M.W.: SG-0: a small standard grid for DFT quadrature on large systems. J. Comput. Chem. 27, 730–739 (2006)
Chiang, L.-Y., Chen, F.-F.: Direct measurement of the angular power spectrum of cosmic microwave background temperature anisotropies in the WAMP data. Astrophys. J. 751, 1–6 (2012)
Chihara, T.S.: Hamburger moment problems and orthogonal polynomials. Trans. Am. Math. Soc. 315, 189–293 (1989)
Child, M.S.: Molecular Collision Theory. Dover, New York (1996)
Clarke, A.S., Shizgal, B.D.: On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients. J. Comput. Phys. 104, 140–149 (1993)
Clayton, D.D.: Principles of Stellar Evolution and Nucleosynthesis. McGraw-Hill, NewYork (1968)
Clenshaw, C., Curtis, A.R.: A method for the numerical integration on an automatic computer. Numer. Math. 2, 197–205 (1960)
Clerk-Maxwell, J.: On approximate multiple integration between limits of summation. Camb. Philos. Soc. Proc. 3, 39–47 (1877)
Cline, J.I., Taatjes, C.A., Leone, S.R.: Diode laser probing of I(2P1/2) Doppler profiles: time evolution of a fast anisotropic velocity distribution in a thermal bath. J. Chem. Phys. 93, 6543–6553 (1990)
Cockburn, B., Karniadakis, G.E., Shu, C.-W.: Discontinuous Galerkin Methods: Theory, Computation and Applications. Springer, Berlin (2000)
Cochran, C., Gelb, A., Wang, Y.: Edge detection from truncated Fourier data using spectral mollifiers. Adv. Comput. Math. 38, 737–762 (2013)
Coffey, W.T., Kalmykov, Y.P., Titov, S.V., Cleary, L.: Quantum effects in the Brownian motion of a particle in a double well potential in the overdamped limit. J. Chem. Phys. 131, 084101 (2009)
Cohen, J.S.: Rapid accurate calculation of JWKB phase-shifts. J. Chem. Phys. 68, 1841–1843 (1978)
Colbert, D.T.,Miller,W.H.: A novel discrete variable representation for quantum-mechanical reactive scattering via the S-Matrix Kohn method. J. Chem. Phys. 96, 1982–1991 (1992)
Collier, M.R.: Are magnetospheric suprathermal particle distributions (κ functions) inconsistent with maximum entropy considerations. Adv. Space Res. 33, 2108–2112 (2004)
Comisarow, M.B.: Fundamental aspects ofFT-ICR and applications to chemistry. Hyperfine Interact. 81, 171–178 (1993)
Comisarow, M.B., Marshall, A.G.: Fourier transform ion cyclotron resonance spectroscopy. Chem. Phys. Lett. 25, 282–283 (1974)
Comtet, A., Bandrauk, A.D., Campbell, D.K.: Exactness of semiclassical bound-state energies for supersymmetric quantum-mechanics. Phys. Lett. B 150, 159–162 (1985)
Concus, P., Cassatt, D., Jaehnig, G., Melby, E.: Tables for the evaluation of int_0^∞ x^α  exp(−x) f (x)dx by Gauss-Laguerre quadrature. Math. Comput. 17, 245–256 (1963)
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
Cools, R.: An encyclopaedia of cubature formulas. J. Complexity 19, 445–453 (2003)
Cools, R.: Constructing cubature formulae: the science behind the art. Acta Numer. 6, 1–54 (1997)
Cools, R.: Advances in multidimensional integration. J. Comput. Appl. Math. 149, 1–12 (2002)
Cooper, F., Ginocchio, J.N., Khare, A.: Relationship between supersymmetry and solvable potentials. Phys. Rev. D 36, 2458–2473 (1987)
Cooper, F., Khare, A., Sukhatme, U.: Supersymmetry and quantum mechanics. Phys. Rep. 251, 267–385 (1995)
Corcoran, C.T., Langhoff, P.W.: Moment-theory approximations for nonnegative spectral densities. J. Math. Phys. 18, 651–657 (1977)
Corngold, N.: Kinetic equation for a weakly coupled test particle. II. Approach to equilibrium. Phys. Rev. A 24, 656–666 (1981)
Crew, G.B., Chang, T.S.: Asymptotic theory of ion conic distributions. Phys. Fluids 28, 2382–2394 (1985)
Cukier, R.I., Lakatos-Lindenberg, K., Shuler, K.E.: Orthogonal polynomial solutions of the Fokker-Planck equation. J. Stat. Phys. 9, 137–144 (1973)
Cuperman, S.,Weiss, J., Dryer,M.:A variational derivation of the velocity distribution functions for nonequilibrium, multispecies, weakly interacting, spherically symmetric many-body systems. J. Stat. Phys 29, 803–812 (1982)


Dadkhahi, H., Gotchev, A., Egiazarian, K.: Inverse polynomial reconstruction method in DCT domain. EURASIP J. Adv. Signal Process. 2012, 1–23 (2012)
Danailov, D.M., Viehland, L.A., Johnson, R., Wright, T.G., Dickinson, A.S.: Transport of O+ through Argon gas.  J. Chem. Phys. 128, 134302 (2008)
Davidovi´c, D.M., Vukani´c, J., Arsenovi´c, D.: Two new analytic approximations of the Chandrasekhar’s H function. Icarus 194, 389–397 (2008)
Davis, P. J. 1963. Interpolation and Approximation , Blaisdell, London.
Davis, P. J. and P. Rabinowitz. 1975. Methods of Numerical Integration, Academic Press.
Davison, B.: Neutron Transport. Oxford University Press, Oxford (1957)
de Groot, S.R., Mazur, P.: Non-equilibrium Thermodynamics. Dover, New York (1984)
Dawes, R., Carrington Jr, T.: A multidimensional discrete variable representation basis obtained by simultaneous diagonalization. J. Chem. Phys. 121, 726–736 (2004)
Dawes, R., Carrington, T.: How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates. J. Chem. Phys. 122, 134101 (2005)
Dekker, H., van Kampen, N.G.: Eigenvalues of a diffusion process with a critical point. Phys. Lett.  A 73, 374–376 (1979)
Delves, L.M., Mohamed, J.L.: Computational Methods for Integral Equations. Cambridge University Press, Cambridge (1985)
Demeio, L., Shizgal, B.: Time dependent nucleation. II. A semiclassical approach. J. Chem. Phys. 98, 5713–5719 (1993)
Demeio, L., Shizgal, B.: A uniform Wentzel-Kramers-Brillouin approach to electron transport in molecular gases. J. Chem. Phys. 99, 7638–7651 (1993b)
Derevianko, A., Luc-Koenig, E., Masnou-Seeuws, F.: Application of B-splines in determining the eigenspectrum of diatomic molecules: robust numerical description of Halo-state and Feshbach molecules. Can. J. Phys. 87, 67–74 (2009)
Desai, R. C.: Non-Gaussian corections to Van Hove’s Gs(r, t) for a monatomic gas, J. Chem. Phys., 44, 77–86 (1966).
Desai, R. C. and Nelkin, M.: Atomic motions in a rigid sphere gas as a problem in neutron transport. Nuc. Sci. Eng., 24, 142–152 (1966)
Descouvemont, P., Adahchour, A., Angulo, C., Coc, A., Vangioni-Flam, E.: Compilation and Rmatrix analysis of Big Bang nuclear reaction rates. At. Data Nucl. Data Tables 88, 203–236 (2004)
Deville, M.O., Fisher, P.F., Mund, E.H.: High Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge (2002)
Dickinson, A.S., Certain, P.R.: Calculation of matrix elements for one-dimensional quantum mechanical problems. J. Chem. Phys. 49, 4209–4211 (1968)
Dickinson, A.S., Shizgal, B.: Comparison of classical and quantum continuum expectation values. Mol. Phys. 30, 1221–1228 (1975)
Drake, G.W.F.: High precision theory of atomic Helium. Phys. Scr. T83, 82–92 (1999)
Drake, G.W.F., Cassar, M.M., Nistor, R.A.: Ground-state energies for helium, H− and Ps−. Phys. Rev. A 65, 054501 (2002)
Driessler, W.: On the spectrum of the Rayleigh piston. J. Stat. Phys. 24, 595–606 (1981)
Driscoll, T.A.: Automatic spectral collocation for integral, integro-differential and integrally reformulated differential equations. J. Comput. Phys. 229, 5980–5998 (2010)
Driscoll, T.A., Fornberg, B.: A Padé based algorithm for overcoming Gibbs phenomenon. Numer. Algorithms 26, 77–92 (2001)
Drozdov, A.N., Tucker, S.C.: An improved reactive flux method for evaluation of rate constants in dissipative systems. J. Chem. Phys. 115, 9675–9684 (2001)
Drozdov, A.N.: Two novel approaches to the Kramers rate problem in the spatial diffusion regime. J. Chem. Phys. 111, 6481–6491 (1999)
Duarte, F.B., Tenreiro Machado, J.A., Duarte, G.M.: Dynamics of the Dow Jones and the NASDAQ stock indexes. Nonlinear Dyn. 61, 691–705 (2010)
Dudynski, M.: Spectral properties of the linearized Boltzmann operator in Lp for 1 ≤ p ≤ ∞. J. Stat. Phys. 153, 1084–1106 (2013)
Dulieu, O., Kosloff, R., Masnou-Seeuws, F., Pichler, G.: Quasibound states in long-range alkali dimers: grid method calculation. J. Chem. Phys. 107, 10633–10642 (1997)
Dunkel, J., Hänggi, P.: Relativistic Brownian motion. Phys. Rep. 471, 1–73 (2009)
Dupuis, M., Marquez, A.: The Rys quadrature revisited: a novel formulation for the efficient computation of electron repulsion integrals over Gaussian functions. J. Chem. Phys. 114, 2067–2078 (2001)
Dupuis, M., Rys, J., King, H.F.: Evaluation of molecular integrals over Gaussian basis functions. J. Chem. Phys. 65, 111–116 (1976)
Durran, D.R.: Numerical Methods for Fluid Dynamics:With Applications to Geophysics. Springer, Berlin (2010)
Dutt, R., Khare, A., Sukhatme, U.P.: Supersymmetry, shape invariance and exactly solvable potentials. Am. J. Phys. 56, 163–168 (1988)
Dyatko, N.A.: Negative electron conductivity in gases and semiconductors. J. Phys.: Conf. Ser. 71, 012005 (2007)
Dyatko, N.A., Loffhagen, D., Napartovich, A.P.,Winkler, R.: Negative electron mobility in attachment dominated plasmas. Plasma Chem. Plasma Proc. 21, 421–439 (2001)
Dziekan, P., Lemarchand, A., Nowakowski, B.:Master equation for a bistable chemical system with perturbed particle velocity distribution function. Phys. Rev. E 85, 021128 (2012)

Echave, J., Clary, D.C.: Potential optimized discrete variable representation. Chem. Phys. Lett. 190, 225–230 (1992)
Echim, M.M., Lemaire, J., Lie-Svendsen, O.: A review on solar wind modeling: kinetic and fluid aspects. Surv. Geophys. 32, 1–70 (2011)
Einstein, A.: Zur theorie der brownschen bewegung. Ann. Phys. 19, 371–381 (1906)
El-Sherbiny, A., Poirier, R.A.:Anevaluation of the radial part of the numerical integration commonly used in DFT. J. Comput. Chem. 25, 1378–1384 (2004)
Ender, A.Ya., Ender, I.A., Bakaleinikov, L.A., Flegontova, E.Yu.: Matrix elements and kernels of the collision integral in the Boltzmann equation. Tech. Phys. 56, 452–463 (2011)
Ernst, M.H.: Nonlinear model Boltzmann equations and exact solutions. Phys. Rep. 78, 1–171 (1981)
Ernst, M.H.: Exact solutions of the nonlinear Boltzmann equation. J. Stat. Phys. 34, 1001–1017 (1984)
Ernst, R.R., Anderson,W.A.: Application of Fourier transform spectroscopy to magnetic resonance. Rev. Sci. Instrum. 37, 93–102 (1966)
Eskola, L.: Geophysical Interpretation Using Integral Equations. Springer, Netherlands (2012)
Evans, G.A.: Some new thoughts on Gauss-Laguerre quadrature. Int. J. Comput. Math. 82, 721–730 (2005)


Fahr, F.J., Shizgal, B.: Modern exospheric theories and their observational relevance. Rev. Geophys. Space Phys. 21, 75–124 (1983)
Fasshauer, G.E., Zhang, J.G.: On choosing optimal shape parameters for RBF approximation. Numer. Algorithms 45, 345–368 (2007)
Feit, M.D., Fleck Jr, J.A., Steiger, A.: Solution of the Schrödinger equation by a spectral method. J. Comput. Phys. 47, 412–433 (1982)
Feizi, H., Rajabi, A.A., Shojaei, M.R.: Supersymmetric solution of the Schrödinger equation for the Woods-Saxon potential using the Pekeris approximation. Acta Phys. Pol. B 42, 2143–2152 (2011)
Felderhof, B.U.: Diffusion in a bistable potential. Physica A 387, 5017–5023 (2008)
Fermi, E.: Un metodo statistico per la determinazione di alcune priopriet dell’atomo. Rend. Accad. Naz. Lincei 6, 602607 (1927)
Ferziger, J.H., Kaper, H.G.: Mathematical Theory of Transport Processes in Gases. North-Holland, Amsterdam (1972)
Filbet, F., Mouhot, C., Pareschi, L.: Solving the Boltzmann equation in Nlog2N. SIAM J. Sci. Comput. 28, 1029–1053 (2006)
Filbet, F., Mouhot, C.: Analysis of spectral methods for the homogeneous Boltzmann equation Trans. Am. Math. Soc. 363, 1947–1980 (2011)
Filbet, F., Russo, G.: High order numerical methods for the space non-homogenous Boltzmann equation. J. Comput. Phys. 186, 457–480 (2003)
Finlayson, B.A.: The Method of Weighted Residuals and Variational Principles. Academic Press, New York (1972)
Finlayson, B.A., Scriven, L.E.: The method of weighted residuals—a review. Appl. Mech. Rev. 19, 735–748 (1966) – Finlayson-Scriven-1966Finlayson-1983
Fiolhais, C., Marques, M.A.L., Nogueira, F.: A Primer in Density Functional Theory. Springer, Berlin (2003)
Fletcher, A.A.J.: Computational Techniques for Fluid Flow. Springer, New York (1991)
Foch, J.D., Ford, G.W.: The linear Boltzmann equation. In: de Boer, J., Uhlenbeck, G.E. (eds.) Studies in Statistical Mechanics, pp. 127–154. Elsevier, Holland (1970)
Fok, J.C.M., Guo, B., Tang, T.: Combined Hermite spectral-finite difference method for the Fokker-Planck equation. Math. Comput. 71, 1497–1528 (2002)
Fokker, A.D.: Die mittlere energie rotierender elektrischer dipole im strahlungsfeld. Ann. Phys. 348, 810–820 (1914)
Ford, G.W.: Matrix elements of the linearized collision operator. Phys. Fluids 11, 515–521 (1968)
Fornberg, B.: A Practical Guide to Pseudospectral Methods. Cambridge University Press, Cambridge (1996)
Fornberg, G., Wright, G., Larsson, E.: Some observations regarding interpolants in the limit of flat radial basis functions. Comput. Math. Appl. 47, 37–55 (2004)
Fornberg, B., Driscoll, T.A., Wright, G., Charles, R.: Observations on the behavior of radial basis function approximations near boundaries. Comput. Math. Appl. 43, 473–490 (2002)
Francisco, J.F.: Internal rotational barriers of ClOOCl. J. Chem. Phys. 103, 8921–8923 (1995)
Frank, T.D.: Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: applications to financial physics and neurophysics. Phys. Lett. A 360, 552–562 (2007)
Frankowski, K., Pekeris, C.L.: Logarithmic terms in the wave functions of two-electron atoms. Phys. Rev. 146, 46–49 (1966)
Fricke, S.H., Balantekin, A.B., Hatchell, P.J., Uzer, T.: Uniform semiclassical approximation to supersymmetric quantum mechanics. Phys. Rev. A 37, 2797–2804 (1988)
Friesner, R.A.: Solution of self-consistent field electronic structure equations by a pseudospectral method. Chem. Phys. Lett. 116, 39–43 (1985)
Friesner, R.A.: New methods for electronic structure calculations on large molecules. Ann. Rev. Phys. Chem. 42, 341–367 (1991)
Friesner, R.A., Bentley, J.A., Menou, M., Leforestier, C.: Adiabatic pseudospectral methods for multidimensional vibrational potentials. J. Chem. Phys. 99, 324–335 (1993)


Gad-el-Hak, M.: The fluid mechanics of microdevices—the Freeman scholar lecture. J. Fluids Eng. 121, 5–33 (1999)
Galant, D.: Gauss quadrature rules for the evaluation of (2/√π) ∞ 0 exp(−x2) f (x)dx. Math. Comput. 23, 674 (1969)
Gallas, J.A.C.: Some matrix elements for Morse oscillator. Phys. Rev. A 21, 1829–1834 (1980)
Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998)
Ganapol, B.D.: Analytical Benchmarks for Nuclear Engineering Applications. Case Studies in Neutron Transport Theory. Nuclear Energy Agency OECD Publications, Paris (2008)
Gander, M.J., Karp, A.H.: Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer. JQRST 68, 213–223 (2001)
Garashchuk, S., Light, J.C.: Quasirandom distributed Gaussian bases for bound problems. J. Chem. Phys. 114, 3929–3939 (2001)
Garcia, R.D.M.: The application of non-classical orthogonal polynomials in particle transport theory. Prog. Nucl. Energy 35, 249–273 (1999)
Garcia, G.A., Nahon, L., Powis, I.: Two-dimensional charged particle image inversion using polar basis function expansion. Rev. Sci. Instrum. 75, 4989–4996 (2004)
Garcia, R.D.M., Siewert, C.E.: A stable shifted-Legendre projection scheme generating PN boundary conditions. Ann. Nucl. Energy 23, 321–332 (1996)
Garg, D., Patterson, M.A., Hager, W.W., Rao, A.V., Benson, D., Huntingdon, G.T.: An overview of three pseudospectral methods for the numerical solution of the optimal control problems. Astrodynamics 135, 475–487 (2009)
Gauss, C.F.: Methodus nova integralium valores per approximationem inveniendi. Comment. Soc. Reg. Scient. Gotting. Recent. 3, 39–76 (1814)
Gardiner, C.W.: Handbook of Stochastic Methods. Springer, Berlin (2003)
Garrity, D.K., Skinner, J.L.: Effect of potential shape on isomerization rate constants for the BGK model. Chem. Phys. Lett. 95, 46–51 (1983)
Gary, S.P.: Theory of Space Plasma Microinstabilities. Cambrigde University Press, Cambridge (1993)
Gautschi, W.: Numerical Analysis, 2nd edn. Birkhäuser, New York (2011)
Gautschi, W.: Variable-precision recurrence coefficients for nonstandard orthogonal polynomials. Numer. Algorithms 52, 409–418 (2009)
Gautschi,W.: The numerical evaluation of a challenging integral. Numer. Algorithms 49, 187–194 (2008)
Gautschi, W.: A guided tour through my bibliography. Numer. Algorithms 45, 11–35 (2007)
Gautschi,W.: Orthogonal Polynomials Computation and Approximation. Oxford University Press, Oxford (2004)
Gautschi, W.: Gauss-Radau formulae for Jacobi and Laguerre weight functions. Math. Comput. Simulat. 54, 403–412 (2000)
Gautschi, W.: Orthogonal polynomials: applications and computation. Acta Numerica 5, 45–119 (1996)
Gautschi,W.: Algorithm 726: ORTHOPOL—a package of routines for generating orthogonal polynomials with Gauss-type quadrature rules. ACM Trans. Math. Softw. 20, 21–62 (1994)
Gautschi,W.: On the computation of generalized Fermi-Dirac and Bose-Einstein integrals. Comput. Phys. Commun. 74, 233–238 (1993)
Gautschi,W.: Orthogonal polynomials-constructive theory and applications. J. Comput. Appl. Math. 12, 61–76 (1985)
Gautschi, W.: Discrete approximations to spherically symmetric distributions. Numer. Math. 44, 53–60 (1984)
Gautschi, W.: A survey of Gauss-Christoffel quadrature formulae. In: Butzer, P.L., Fehér, F. (eds.) E. B. Christoffel, pp. 72–147. Birkhaüser Verlag, Basel (1981)
Gautschi, W.: On the construction of Gaussain quadrature rules from modified moments. Math. Comput. 24, 245–260 (1970)
Gelb, A., Tanner, J.: Robust reprojection methods for the resolution of the Gibbs phenomenon. Appl. Comput. Harmon. Anal. 20, 3–25 (2006)
Gelb, A., Hines, T.: Recovering exponential accuracy from non-harmonic Fourier data through spectral reprojection. J. Sci. Comput. 51, 158–182 (2012)
Gentleman, W.M.: Implementing Clenshaw-Curtis quadrature. I Methodology and experience. Commun. ACM 15, 337–342 (1972)
Ghiroldi, G.P., Gibelli, L.: A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization. J. Comput. Phys. 258, 568–584 (2014)
Ghosh, K.: Analytical benchmark for non-equilibrium radiation diffusion in finite size systems. Ann. Nucl. Energy 63, 59–68 (2014)
Gibble, K.E., Gallagher, A.: Measurements of velocity-changing collision kernels. Phys. Rev. A 43, 1366–1380 (1991)
Gibelli, L.: Velocity slip coefficients based on the hard-sphere Boltzmann equation. Phys. Fluids 24, 022001 (2012)
Gibelli, L., Shizgal, B.D.: Spectral convergence of the Hermite basis function solution of the Vlasov equation, the free-streaming term. J. Comput. Phys. 219, 477–488 (2006)
Gibelli, L., Shizgal, B.D., Yau, A.W.: Ion energization by wave-particle interactions: comparison of spectral and particle simulation solutions of the Vlasov equation. Comput. Math. Appl. 59, 2566–2581 (2010)
Gifford, K.A.,Horton Jr, J.L.,Wareing,T.A., Failla, G., Mourtada, F.: Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations. Phys. Med. Biol. 51, 2253–2265 (2006)
Gill, P.M.W.: Molecular integrals over Gaussian basis functions. Adv. Quant. Chem. 25, 141–205 (1994)
Gil, A., Segura, J., Temme, N.M.: Numerical Methods for Special Functions. SIAM, Philadelphia (2007)
Gill, P.M.W., Chien, S.-H.: Radial quadrature for multiexponential integrands. J. Comput. Chem. 24, 732–740 (2003)
Gillespie, G.T.: Approximating the master equation by Fokker-Planck type equations for single variable chemical systems. J. Chem. Phys. 72, 5363–5370 (1980)
Gillespie, G.T.: Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral. Phys. Rev. E 54, 2084–2091 (1996)
Gitterman, M.: Simple treatment of correlated multiplicative and additive noises. J. Phys. A: Math. Gen. 32, L293–L297 (1999)
Goldstein, H., Poole, C., Safko, J.: Classical Mechanics. Addison Wesley, San Francisco (2000)
Golub, G.H.: Some modified matrix eigenvalue problems. SIAM Rev. 15, 318–334 (1973)
Golub, G.H., Meurant, G.: Matrices, Moments and Quadrature with Applications. Princeton University Press, Princeton (2009)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)
Golub, G.H., Welsch, J.H.: Calculation of Gauss quadrature rules. Math. Comput. 23, 221–230 (1969)
Gombosi, T.I.: Gaskinetic Theory. Cambridge University Press, Cambridge (1994)
Gomes, P.C., Pacios, L.F.: The torsional barrier of ClOOCl. J. Phys. Chem. 100, 8731–8736 (1996)
Gomez-Ullate, D., Kamran, N., Milson, R.: An extended class of orthogonal polynomials defined by a Sturm-Liouville problem. J. Math. Anal. Appl. 359, 352–376 (2009)
Gordon, R.G.: Error bounds in equilibrium statistical mechanics. J. Math. Phys. 9, 655–663 (1968)
Gottlieb, D., Orszag, S.: Numerical Analysis of Spectral Methods: Theory and Applications. SIAM, Philadelphia (1977)
Gottlieb, D., Shu, C.-W.: On the Gibbs phenomenon and its resolution. SIAM Rev. 39, 644–668 (1997)
Gottlieb, D., Shu, C.-W., Solomonoff, A., Vandeven, H.: On the Gibbs phenomenon 1: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. J. Comput. Appl. Math. 43, 81–98 (1992)
Gottlieb, D., Gustafsson, B., Forssén, P.: On the direct Fourier method for computer tomography. IEEE Trans. Med. Imaging 19, 223–232 (2000)
Gottlieb, D., Hesthaven, J.S.: Spectral methods for hyperbolic problems. J. Comput. Appl. Math. 128, 83–131 (2001)
Gottlieb, S., Jung, J.H., Kim, S.: A review of David Gottlieb’s work on the resolution of the Gibbs phenomenon. Commun. Comput. Phys. 9, 497–519 (2011)
Grabowski, P.E., Chernoff, D.F.: Pseudospectral calculation of helium wave functions, expectation values, and oscillator strength. Phys. Rev. A 84, 042505 (2011)
Grad, H.: Principles of the kinetic theory. In: Handbook of Physics, pp. 205–294. Springer, Berlin (1958)
Grad, H.: On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2, 331–407 (1949)
Grad, H.: Asymptotic theory of the Boltzmann equation. Phys. Fluids 6, 147–181 (1963)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products. Elsevier, Amsterdam (2007)
Grandclément, P., Novak, J.: Spectral methods for numerical relativity. Living Rev. Relativity 12, 1–103 (2009)
Graur, I.A., Polikarpov, A.P.: Comparison of different kinetic models for the heat transfer problems. Heat Mass Transf. 46, 237–244 (2009)
Gross, E.P., Jackson, E.A., Ziering, S.: Boundary value problems in kinetic theory of gases. Ann. Phys. 1, 141–167 (1957)
Gross, E.P., Ziering, S.: Kinetic theory of linear shear flow. Phys. Fluids 1, 215–224 (1958)
Guantes, R., Farantos, S.C.: High order finite difference algorithms for solving the Schrödinger  equation. J. Chem. Phys. 111, 10827–10835 (1999)
Gunther, L., Weaver, D.L.: Monte Carlo simulation of Brownian motion with viscous drag. Am. J. Phys. 46, 543–545 (1978)
Gust, E.D., Reichl, L.E.: Molecular dynamics simulation of collision operator eigenvalues. Phys. Rev. E 79, 031202 (2009)
Gust, E.D., Reichl, L.E.: Relaxation rates of the linearized Uehling-Uhlenbech equation for bosons. Phys. Rev. E 81, 061202 (2010)


Haberman, R.: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th edn. Prentice Hall, Upper Saddle River (2013)
Hagelaar, G.J.M., Pitchford, L.C.: Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Sci. Technol. 14, 722–733 (2005)
Hamilton, I.P., Light, J.C.: On distributed Gaussian bases for simple model multidimensional vibrational problems. J. Chem. Phys 84, 306–317 (1986)
Hammer, P.C., Wymore, A.W.: Numerical evaluation of multiple integrals I. Math. Comput. 11, 59–67 (1957)
Hammer, P.C., Stroud, A.H.: Numerical evaluation of multiple integrals II. Math. Comput. 12, 272–280 (1958)
Hanna, J.R., Rowland, J.H.: Fourier Series, Transforms, and BoundaryValue Problems. Dover, New York (2008)
Hänggi, P., Talkner, P., Borkovec, M.: Reaction rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990)
Harris, D.O., Engerholm, G.G., Gwinn,W.D.: Calculation of matrix elements for one-dimensional quantum-mechanical problems and the application to anharmonic oscillators. J. Chem. Phys. 43, 1515–1517 (1965)
Hasegawa, A., Mima, K., Duong-van, M.: Plasma distribution function in a superthermal radiation field. Phys. Rev. Lett. 54, 2608–2610 (1985)
Hau, L.-N., Fu, W.-Z.: Mathematical and physical aspects of Kappa velocity distribution. Phys. Plasmas 14, 110702 (2007)
Hau, L.-N., Fu,W.-Z., Chuang, S.-H.: Response to Comment on mathematical and physical aspects of Kappa velocity distribution. Phys. Plasmas 16, 094702 (2009)
Haubold, H.J., John, R.W.: Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys. 23, 399–411 (1981)
Haxton, D.J.: Lebedev discrete variable representation. J. Phys. B: At. Mol. Opt. Phys. 40, 4443– 4451 (2007)
Hebert, A.: Applied Reactor Physics. Presse Internationales Polytechnique, Montréal (2009)
Heidbrink, W.W., Sadler, G.J.: The behaviour of fast ions in Tokamak experiments. Nucl. Fusion 34, 535–615 (1994)
Heintz, A., Kowalczyk, P., Grzhibovskis, R.: Fast numerical method for the Boltzmann equation on non-uniform grids. J. Comput. Phys. 227, 6681–6695 (2008)
Helgaker, T., Jorgensen, P., Olsen, J.: Molecular Electronic Structure Theory. Wiley, New York (2000)
Hellberg, M.A., Mace, R.L., Baluku, T.K., Kourakis, I., Saini, N.S.: Comment on mathematical and physical aspects of Kappa velocity distribution. Phys. Plasmas 16, 094701 (2009)
Helmberg, G.: Introduction to Spectral Theory in Hilbert Space. Dover, New York (2008)
Henon, M., Heiles, C.: The applicability of the third integral of motion: some numerical experiments. Astron. J. 69, 73–79 (1964)
Herman, A.L., Conway, B.A.: Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules. J. Guid. Control Dyn. 19, 592–599 (1996)
Hermann, M.R., Langhoff, P.W.: Explicit Hilbert space representation of Schrödinger states: definitions and properties of Stieltjes-Tchebycheff orbitals. J. Math. Phys. 24, 541–547 (1983)
Hesthaven, J.S.: Integration preconditioning of pseudospectral operators. I. Basic linear operators. SIAM J. Numer. Anal. 35, 1571–1593 (1998)
Hesthaven, J.S., Gottlieb, S., Gottlieb, D.: Spectral Methods for Time Dependent Problems. Cambridge University Press, Cambridge (2007)
Hewitt, E., Hewitt, R.E.: The Gibbs-Wilbraham phenomenon: an episode in Fourier analysis. Arch. Hist. Exact Sci. 21, 129–160 (1979)
Heyl, J.S., Thirumalai, A.: Pseudo-spectral methods for atoms in strong magnetic fields. Mon. Not. R. Astron. Soc. 407, 590–598 (2010)
Hill, R.N.: Rates of convergence and error estimation formulas for the Rayleigh-Ritz variational methods. J. Chem. Phys. 83, 1173–1196 (1985)
Hinton, F.L.: Collisional transport in plasma. In: Galeev, A.A., Sagdeev, R.Z. (eds.) Handbook of Physics, Basic Plasma Physics, pp. 147–197. Elsevier, The Netherlands (1983)
Hiroi, T.: Recalculation of the isotropic H functions. Icarus 109, 313–317 (1994)
Hirschfelder, J.O., Curtiss, C.F., Bird, B.: The Molecular Theory of Gases and Liquids.Wiley, New York (1954)
Hoare, M.R.: The linear gas. Adv. Chem. Phys. 20, 135–214 (1971)
Hoare, M.R., Kaplinsky, C.H.: Linear hard sphere gas: variational eigenvalue spectrum of the energy kernel. J. Chem. Phys. 52, 3336–3353 (1970)
Hoffman, D.K.,Wei, G.W., Zhang, D.S., Kouri, D.J.: Interpolating distributed approximating functionals. Phys. Rev. E 57, 6152–6160 (1998)
Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964)
Holloway, J.P.: Spectral discretizations of the Vlasov-Maxwell equations. Trans. Theory Stat. Phys. 25, 1–32 (1996)
Holway, L.H.: Time varying weight functions and the convergence of polynomial expansions. Phys. Fluids 10, 35–48 (1967)
Hrycak, T., Grchenig, K.: Pseudospectral Fourier reconstruction with the modified inverse polynomial reconstruction method. J. Comput. Phys. 229, 933–946 (2010)
Hu, X.G., Ho, T.S., Rabitz, H., Askar, A.: Solution of the quantum fluid dynamical equations with radial basis function interpolation. Phys. Rev. E 61, 5967–5976 (2000)
Hu, X.G., Ho, T.S., Rabitz, H., Askar, A.: Multivariate radial basis interpolation for solving quantum fluid dynamical equations. Comput. Math. Appl. 43, 525–537 (2002)
Huang, K.: Statistical Mechanics. Wiley, New York (1967)
Hubert, D.: Auroral ion velocity distribution function: generalized polynomial solution of Boltzmann’s equation. Planet. Space Sci. 31, 119–127 (1983)
Huang, A.B., Giddens, D.P.: A new table for a modified (half-range) Gauss-Hermite quadrature with an evaluation of integral. J. Math. Phys. 47, 213–218 (1968)
Hunter, J.K., Nachtergaele, B.: Applied Analysis. World Scientific, Singapore (2001)
Hunter, C.: Spectral analysis of orbits via discrete Fourier transforms. Space Sci. Rev. 102, 83–99 (2002)
Hurn, A.S., Jeisman, J.I., Lindsay, K.A.: Seeing the wood for the trees: a critical evaluation of methods to estimate the parameters of stochastic differential equations. J. Financ. Econ. 5, 390– 455 (2007)
Hussein, M.S., Pato, M.P.: Uniform expansion of the thermonuclear reaction rate formula. Braz. J. Phys. 27, 364–372 (1997)


Isaacson, S.A., Kirby, R.M.: Numerical solution of linear Volterra integral equations of the second kind with sharp gradients. J. Comput. Appl. Math. 235, 4283–4301 (2011)
Iserles, A., Norsett, S.P.: Efficient quadrature of highly oscillatory integrals using derivatives. Proc. R. Soc. A 461, 1383–1399 (2005)


Jablonski, A.: Improved algorithm for calculating the Chandrasekhar function. Comput. Phys. Commun. 184, 440–442 (2013)
James, J.F.: A Student’s Guide to Fourier Transforms, 2nd edn. Cambridge University Press, Cambridge (2002)
Jamieson, M.J., Dalgarno, A., Wei, L.: Elastic scattering of hydrogen and deuterium atoms by oxygen atoms. J. Geophys. Res. 111, A06308 (2006)
Jerri, A.J.: The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations. Kluwer, Boston (1998)
Jerri, A.J.: Introduction to Integral Equations with Applications, 2nd edn.Wiley, New York (1999)
Jerri, A.J.: Advances in Gibbs Phenomenon. Sampling, Potsdam (2011)
Jirari, A.: Second order Sturm-Liouville difference equations and orthogonal polynomials. Mem. Am. Math. Soc. 113(542), (1995)
Johnson, B.R.: New numerical methods applied to solving the one dimensional eigenvalue problem. J. Chem. Phys. 67, 4086–4093 (1977)
Johnson, R.E., Liu, M., Tully, C.: Collisional dissociation cross sections for O + O2, CO+ N2, O2 + O2, N + N2 and N2 + N2. Planet. Space Sci. 50, 123–128 (2002)
Jones, R.O., Gunnarsson, O.: The density functional formalism, its applications and prospects. Rev Mod. Phys. 61, 689–746 (1989)
Jung, J.-H., Shizgal, B.D.: Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon. J. Comput. Appl. Math. 172, 131–151 (2004)
Jung, J.-H., Shizgal, B.D.: Inverse polynomial reconstruction of two dimensional Fourier images. J. Sci. Comput. 25, 367–399 (2005)
Jung, J.-H., Shizgal, B.D.: On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon. J. Comput. Phys. 224, 477–488 (2007)
Jung, K.-J., Zhao, T.: Parallel imaging with asymmetric acceleration to reduce Gibbs artifacts and to increase signal-to-noise ratio of the gradient echo echo-planar imaging sequence for functional MRI. Magn. Reson. Med. 67, 419–427 (2012)
Jung, J.-H., Stefan, W.: A simple regularization of the polynomial interpolation for the resolution of the Runge phenomenon. J. Sci. Comput. 46, 225–242 (2011)
Jung, J.-H., Gottlieb, S., Kim, S.O.: Iterative adaptive RBF methods for detection of edges in two-dimensional functions. Appl. Numer. Math. 61, 77–91 (2011)

Jüngel, A.: Transport Equations for Semiconductors. Springer, New York (2009)


Kabin, K., Shizgal, B.D.: Exact evaluation of collision integrals for the nonlinear Boltzmann equation. AIP Conf. Proc. 663, 35–42 (2003)
Kakhiani, K., Tsereteli, K., Tsereteli, P.:A program to generate a basis set adaptive radial quadrature grid for density functional theory. Comput. Phys. Commun. 180, 256–268 (2009)
Kallush, S., Kosloff, R.: Improved methods for mapped grids: applied to highly excited vibrational states of diatomic molecules. Chem. Phys. Lett. 433, 221–227 (2006)
Kamm, J.R.,Williams, T.O., Brock, J.S., Li, S.: Application of Gegenbauer polynomial expansions to mitigate Gibbs phenomenon in Fourier-Bessel series solutions of a dynamic sphere problem. Int. J. Numer. Meth. Biomed. Eng. 26, 1276–1292 (2010)
Kan, M.W.K., Yu, P.K.N., Leung, L.H.T.: A review on the use of grid-based Boltzmann equation solvers for dose calculation in external photon beam treatment planning. Biomed. Res. Int. 2013, 692874 (2013)
Kapral, R., Ross, J.: Relaxation in a dilute binary gas mixture. J. Chem. Phys. 52, 1238–1243 (1970)
Karabulut, H., Kalay, M.: Distributed Gaussian discrete variable representation. J. Quant. Chem. 104, 16–28 (2005)
Karney, C.F.F.: Fokker-Planck and quasi-linear codes. Comput. Phys. Rep. 4, 183–244 (1986)
Karplus, M., Porter, R.N.: Atoms and Molecules: An Introduction for Students of Physical Chemistry Benjamin, Menlo Park (1970)
Kawabata, K., Limaye, S.S.: Rational approximation formula for Chandrasekhar’s H-function for isotropic scattering. Astrophys. Space Sci. 332, 365–371 (2011)
Kaur, P., Kumaran, S.S., Tripathi, R.P., Khushu, S., Kaushik, S.: Protocol error artifacts in MRI: sources and remedies revisited. Radiography 13, 291–306 (2007)
Kawabata, K., Satoh, T., Ueno, S.: A direct numerical approach to the Chandrasekhar’s H-function for arbitrary characteristic functions. Astrophys. Space Sci. 182, 249–260 (1991)
Kennedy, M., Smith, F.J.: The efficient computation of JWKB phase shifts. Mol. Phys. 13, 443–448 (1967)
Kern, C.W., Karplus, M.: Gaussian-transform method for molecular integrals. II. Evaluation of molecular properties. J. Chem. Phys. 43, 415–429 (1965)
Kharchenko,V., Tharamel, J., Dalgarno, A.: Kinetics of thermalization of fast nitrogen atoms beyond the hard sphere approximation. J. Atmos. Sol. Terr. Phys. 59, 107–115 (1997)
Kharchenko, V., Balakrishnan, N., Dalgarno, A.: Thermalization of fast nitrogen atoms in elastic and inelastic collisions with molecules of atmospheric gases. J. Atmos. Terr. Phys. 60, 95–106 (1998)
Kharchenko, V., Dalgarno, A.: Thermalization of fast O(1D) atoms in the stratosphere and mesosphere. J. Geophys. Res. 109, D18311 (2004)
Khazanov, G.V.: Kinetic Theory of the Inner Magnetospheric Plasma. Springer, New York (2011)
King, H.F., Dupuis, M.: Numerical integration using Rys polynomials. J. Comput. Phys. 21, 144–165 (1976)
Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965)
Khurana, S., Thachuk, M.: A numerical solution of the linear Boltzmann equation using cubic B-splines. J. Chem. Phys. 136, 094103 (2012)
Khurana, S., Thachuk, M.: Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles. J. Chem. Phys. 139, 164122 (2013)
Kim, J.G., Boyd, I.D.: State-resolved master equation analysis of thermochemical nonequilibrium of nitrogen. Chem. Phys. 415, 237–246 (2013)
Knessl, C., Mangel, M., Matkowsky, B.J., Schuss, Z., Tier, C.: Solution of Kramers-Moyal equations for problems in chemical physics. J. Chem. Phys. 81, 1285–1293 (1984)
Knierim, K.D., Waldman, M., Mason, E.A.: Moment theory of electron thermalization in gases. J. Chem. Phys. 77, 943–950 (1982)
Koay, C.G., Sarlls, J.E., Özarslan, E.: Three-dimensional analytical magnetic resonance imaging phantom in the Fourier domain. Magn. Reson. Med. 58, 430–436 (2007)
Kokoouline, V., Dulieu, O., Kosloff, R., Masnou-Seeuws, F.: Mapped Fourier methods for long range molecules: application to perturbations in the Rb2(0+u ) photoassociation spectrum. J. Chem. Phys. 110, 9865–9876 (1999)
Kopriva, D.A.: Implementing Spectral Methods for Partial Differential Equations Algorithms for Scientists and Engineers. Springer, Berlin (2009)
Koput, J., Carter, S., Handy, N.C.: Ab initio prediction of the vibrational-rotational energy levels of hydrogen peroxide and its isotopomers. J. Chem. Phys. 115, 8345–8350 (2001)
Kosloff, R.: Propagation methods for quantum molecular dynamics. Annu. Rev. Phys. Chem. 45, 145–178 (1994)
Kosloff, R.: The Fourier method. In: Cerjan, C. (ed.) Numerical Grid Methods and Their Application to Schrödinger’s Equation, pp. 175–194. Kluwer Academic, The Netherlands (1993)
Kosloff, D., Kosloff, R.: A Fourier method solution for the time-dependent Schrödinger equation as a tool in molecular dynamics. J. Comput. Phys. 52, 35–53 (1983)
Kourganoff, V.: Basic Methods in Transfer Problems. Oxford University Press, Oxford (1963)
Koura, K.: Nonequilibrium electron velocity distribution and temperature in thermalization of low energy electrons in molecular hydrogen. J. Chem. Phys. 79, 3367–3372 (1983)
Kowari, K., Demeio, L., Shizgal, B.: Electron degradation and thermalization in CH4 gas. J. Chem. Phys. 97, 2061–2074 (1992)
Kowari, K., Shizgal, B.: On the existence of a steady electron distribution for systems with electron attachment: Ar-CCl4 mixtures. Chem. Phys. Lett. 260, 365–370 (1996)
Kowari, K.-I., Leung, K., Shizgal, B.D.: The coupling of electron thermalization and electron attachment in CCl4/Ar and CCl4/Ne mixtures. J. Chem. Phys. 108, 1587–1600 (1998)
Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)
Kuczka, J., Hänggi, P., Gadmski, A.: Non-Markovian process driven quadratic noise: Kramers-Moyal expansion and Fokker-Planck modeling. Phys. Rev. E 51, 2933–2938 (1995)
Kremer, G.M.: An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer, New York (2010)
Krook, M., Wu, T.T.: Formation of Maxwellian tails. Phys. Rev. Lett. 36, 1107–1109 (1976)
Krupp, R.S.:A nonequilibrium solution of the Fourier transformed Boltzmann equation. MSc thesis, MIT (1967)
Kügerl, G., Schürrer, F.: On the relaxation of binary hard-sphere gases. Phys. Fluids A2, 609–618 (1990)
Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22, 79–86 (1951)
Kumar, A.S.: An analytical solution to applied mathematics-related Loves equation using the Boubaker polynomials expansion scheme. J. Frankl. Inst. 347, 1755–1761 (2010)
Kumar, K., Skullerud, H.R., Robson, R.E.: Kinetic theory of charged particle swarms in neutral gases. Aust. J. Phys. 33, 343–448 (1980)
Kundu, P., Cohen, I.M., Dowling, D.R.: Fluid Mechanics, 6th edn. Academic Press,Waltham (2012)
Kušˇcer, I., Corngold, N.: Discrete relaxation times in neutron transport. Phys. Rev. 139, A981–A990 (1965)
Kušˇcer, I., Williams, M.M.R.: Relaxation constants of a uniform hard sphere gas. Phys. Fluids 10, 1922–1927 (1967)
Kušˇcer, I., McCormick, N.J.: Some analytical results for radiative transfer in thick atmospheres. Trans. Theory Stat. Phys. 20, 351–381 (1991)
Kustova, E.V., Giordano, D.: Cross-coupling effects in chemically non-equilibrium viscous compressible flows. Chem. Phys. 379, 83–91 (2011)
Kythe, P.K., Puri, P.: Computational Methods for Linear Integral Equations. Birkhauser, Berlin (2002)
Kythe, P.K., Schaferkotter, M.R.: Handbook of Computational Methods for Integration. Chapman and Hall/CRC, London (2004)


Lanczos, C.: Discourse on Fourier Series. Hafner, New York (1966)
Landau, D.P., Binder, K.: A Guide to Monte Carlo Simulations in Statistical Physics, 3rd edn. Cambridge University Press, Cambridge (2009)
Langer, R.E.: On the connection formulas and the solutions of the wave equation. Phys. Rev. 51, 669–676 (1937)
Langhoff, P.W., Corcoran, C.T., Sims, J.S., Weinhold, F., Glover, R.M.: Moment-theory ofphotoabsorption and dispersion profiles in atoms and ions. Phys. Rev. A 14, 1042–1056 (1976)
Larsen, E.W., Livermore, C.D., Pomraning, G.C., Sanderson, J.G.: Discretization methods for one dimensional Fokker-Planck operators. J. Comput. Phys. 61, 359–390 (1985)
Larson, R.S., Kostin, M.D.: Kramers’s theory of chemical kinetics: eigenvalue and eigenfunction analysis. J. Chem. Phys. 69, 4821–4829 (1978)
Laskar, J.: Frequency analysis for multi-dimensional systems. Global dynamics and diffusion. Physica D 67, 257–281 (1993)
Laskar, J., Correia, A.C.M.: HD60532, a planetary system in a 3:1 mean motion resonance. Astron. Astrophys. 496, L4–L8 (2009)
Lathrop, K.D.: The early days of the SN method. Am. Nucl. Soc. Trans. 66, 241–242 (1992)
Lauvergnat, D., Nauts, A.: Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality. Spectrochim. Acta, A 119, 18–25 (2014)
Lax, M.: Classical noise IV: Langevin method. Rev. Mod. Phys. 38, 541–566 (1966)
Layton, E.G.: The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory. J. Phys. B: At. Mol. Opt. Phys. 26, 2501–2522 (1993)
Le, H.M., Huynh, S., Raff, L.: Molecular dissociation of hydrogen peroxide (HOOH) on a neural network ab initio potential surface with a new configuration sampling method involving gradient fitting. J. Chem. Phys. 131, 014107 (2009)
Lebedev, V.I.: Spherical quadrature formulas exact to orders 25–29. Sib. Mat. Zh. 18, 132–142 (1977)
Leblanc, F., Hubert, D.: A generalized model for the proton expansion in astrophysical winds. I. The velocity distribution function representation. Astrophys. J. 483, 464–474 (1997)
Le Bourdiec, S., de Vuyst, F., Jacquet, L.: Numerical solution of the Vlasov-Poisson system using generalized Hermite functions. Comput. Phys. Commun. 175, 528–544 (2006)
Lemmon, E.W., Jacobsen, R.T.:Viscosity and thermal conductivity equations for Nitrogen, Oxygen, Argon, and Air. Int. J. Thermophys. 25, 21–69 (2004)
Le Mouël, J.-L., Shnirman, M.G., Blanter, E.M.: The 27-day signal in sunspot number series and the solar dynamo. Sol. Phys. 246, 295–307 (2007)
Lemaire, J.: Half a century of kinetic solar wind models. AIP Conf. Proc. 1216, 8–13 (2010)
Lemaire, J., Scherer, M.: Model of the polar ion exosphere. Planet. Space Sci. 18, 103–120 (1970)
Lemaire, J., Scherer, M.: Kinetic models of the solar and polar winds. Rev. Geophys. Space Phys. 11, 427–468 (1973)
Lemou, M., Chavanis, P.H.: Escape of stars from gravitational clusters in the Chandrasekhar model. Physica A 389, 1021–1040 (2010)
Leubner, M.P., Vörös, Z.: A nonextensive entropy approach to solar wind intermittency. Astrophys. J. 618, 547–555 (2005)
Leung, K., Shizgal, B.D., Chen, H.: The quadrature discretization methodQDMin comparison with other numerical methods of solution of the Fokker-Planck equation for electron thermalization. J. Math. Chem. 24, 291–319 (1998)
LeVeque, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, Philadelphia (2007)
Levine, I.N.: Quantum Chemistry, 6th edn. Prentice Hall, New Jersey (2009)
Liao, P.F., Bjorholm, J.E., Berman, P.R.: Effects of velocity-changing collisions on two-photon and stepwise-absorption spectroscopic line shapes. Phys. Rev. A 21, 1927–1938 (1980)
Liang, S.: Quantitative Remote Sensing of Land Surfaces. Wiley, New Jersey (2005)
Liboff, R.L.: Introductory Quantum Mechanics, 4th edn. Addison-Wesley, New York (2002)
Liboff, R.L.: Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, 3rd edn. Springer, New York (2003)
Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 53, 603–641 (1981)
Lie-Svendsen, O., Rees, M.H.: An improved kinetic model for the polar outflow of a minor ion. J. Geophys. Res. 101, 2415–2433 (1996)
Light, J.C., Hamilton, I.P., Lill, J.V.: Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys. 82, 1400–1409 (1985)
Light, J.C., Carrington Jr, T.: Discrete variable representations and their utilization. Adv. Chem. Phys. 114, 263–310 (2000)
Lightman, A.P., Shapiro, S.L.: The dynamical evolution of globular clusters. Rev. Mod. Phys. 50, 437–481 (1978)
Lin, S.Y., Guo, H.: Exact quantum mechanical calculations of rovibrational energy levels of hydrogen peroxide (HOOH). J. Chem. Phys. 119, 5867–5873 (2003)
Lin, S.R., Robson, R.E., Mason, E.A.: Moment theory of electron drift and diffusion in neutral gases in an electrostatic field. J. Chem. Phys. 71, 3483–3498 (1979)
Lin, S.Y., Viehland, L.A., Mason, E.A.: Three temperature theory of gaseous ion transport. Chem. Phys. 37, 411–424 (1979)
Lindenfeld, M.J., Shizgal, B.: Matrix elements of the Boltzmann collision operator for gas mixtures. Chem. Phys. 41, 81–95 (1979)
Lindenfeld, M.J., Shizgal, B.: Non-Maxwellian effects associated with the thermal escape of a planetary atmosphere. Planet. Space Sci. 27, 739–751 (1979)
Lindenfeld, M.J., Shizgal, B.: The Milne problem: a study of the mass dependence. Phys. Rev. A27, 1657–1670 (1983)
Lindfield, G.R., Penny, J.E.T.: Numerical Methods Using MATLAB. Elsevier, Amsterdam (2012)
Lindh, R., Malmqvist, P.A., Gagliardi, L.: Molecular integrals by numerical quadrature I. Radial integration. Theor. Chem. Acta 106, 178–187 (2001)
Liou, K.-N.: A numerical experiment on Chandrasekhar’s discrete-ordinate method for radiative transfer: applications to cloudy and hazy atmospheres. J. Atmos. Sci. 30, 1303–1326 (1973)
Liou, K.N.: An Introduction to Atmospheric Radiation. Elsevier, Amsterdam (2002)
Liu, Q.-J., Zhao,W.-Q.: Iterative solution for groundstate of H+2 ion. Commun. Theor. Phys (Beijing, China). 53, 57–62 (2010)
Littlejohn, R.G., Cargo, M., Carrington Jr, T., Mitchell, K.A., Poirier, B.: A general framework for discrete variable representation basis sets. J. Chem. Phys. 116, 8691–8703 (2002)
Livadiotis, G., McComas, D.J.: Beyond Kappa distributions: exploiting Tsallis statistical mechanics in space plasmas. J. Geophys. Res. 114, A11105 (2009)
Lo, J.Q.-W., Shizgal, B.D.: Spectral convergence of the quadrature discretization method in the solution of the Schrödinger and Fokker-Planck equations: comparison with Sinc methods. J. Chem. Phys. 125, 194108 (2006)
Lo, J.Q.-W., Shizgal, B.D.: An efficient mapped pseudospectral method for weakly bound states: vibrational states of He2, Ne2, Ar2 and Cs2. J. Phys. B: At. Mol. Opt. Phys. 41, 185103 (2008a)
Lo, J.Q.-W., Shizgal, B.D.: Pseudospectral methods of solution of the Schrödinger equation. J. Math. Chem. 44, 787–801 (2008)
Love, E.R.: The electrostatic field of two equal circular co-axial conducting disks. Q. J.Mech. Appl. Math. 2, 428–451 (1949)
Lowke, J.J., Tanaka, M.: LTE-diffusion approximation for arc calculations. J. Phys. D: Appl. Phys. 39, 3634–3643 (2006)
Loyalka, S.K., Naz, S.: Milne’s half-space problem: a numerical solution of the related integral equation. Ann. Nucl. Energy 35, 1900–1902 (2008)
Loyalka, S.K., Tipton, E.L., Tompson, R.V.: Chapman-Enskog solutions to arbitrary order in Sonine polynomials I: simple, rigid-sphere gas. Physica A 379, 417–435 (2007)
Lutsko, J.F., Boon, J.P.: Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems. EPL 95, 20006 (2011)
Lynch, V.A., Mielke, S.L., Truhlar, D.G.: Accurate vibrational-rotational partition functions and standard-state free energy values for H2O2 from Monte Carlo path-integral calculations. J. Chem. Phys. 121, 5148–5162 (2004)
Lyness, J.N.: When not to use an automatic quadrature routine. SIAM Rev. 25, 63–87 (1983)
Lyness, J.N.: Integrating some infinite oscillating tails. J. Comput. Appl.Math. 12, 109–117 (1985)


Ma, C.-Y., Summers, D.: Formation of power-law energy spectra in space plasmas by stochastic acceleration due to Whistler-mode waves. Geophys. Res. Lett. 26, 1121-1124 (1999)
Ma, J.Z.G., St.-Maurice, J.-P.: Ion distribution functions in cylindrically symmetric electric fields in the auroral ionosphere: the collision-free case in a uniformly charged configuration. J. Geophys. Res. 113, A05312 (2008)
Magnus, A.P., Pierrard, V.: Formulas for the recurrence coefficients of orthogonal polynomials related to Lorentzian-like weights. J. Comput. Appl. Math. 219, 431–440 (2008)
Maksimovic,M., Pierrard,V., Lemaire, J.:Akinetic model of the solar wind with Kappa distributions in the corona. Astron. Astrophys. 324, 725–734 (1997)
March, R., Barone, P.: Reconstruction of a piecewise constant function from noisy Fourier coefficients by Padé method. SIAM J. Appl. Math. 60, 1137–1156 (2000)
Marechal, E., Moreau, M.: On the microscopic kinetic theory of a chemical reaction in the limit of high collision frequency. Mol. Phys. 51, 133–140 (1984)
Marsch, E.: Kinetic physics of the solar corona and solar wind. Living Rev. Sol. Phys. 3, 1–100 (2006)
Martens, J.: The Hermite transform: a survey. J. Appl. Signal Proc. 2006, 1–20 (2006)
Marston, C.C., Balint-Kurti, G.G.: The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions. J. Chem. Phys. 91, 3571–3576 (1989)
Mason, E.A., McDaniel, E.W.: Transport Properties of Ions in Gases. Wiley, New York (1988)
Matsuyama, H., Koga, T.: Inner and outer radial density functions in singly-excited 1sn states of the He atom. J. Comp. Appl. Math. 233, 1584–1589 (2010)
Mathai, A.M., Haubold, H.J.: Review of mathematical techniques applicable in astrophysical reaction rate theory. Astrophys. Space Sci. 282, 265–280 (2002)
Matsumi, Y., Shamsuddin, S.M., Sato, Y., Kawasaki, M.: Velocity relaxation of hot O(1D) atoms by collisions with rare gases, N2, and O2. J. Chem. Phys. 101, 9610–9618 (1994)
Mazziotti, D.A.: Spectral difference methods for solving differential equations. Chem. Phys. Lett. 299, 473–480 (1999)
McCormick, N.J., Kušˇcer, I.: Singular eigenfunction expansions in neutron transport problems. Adv. Nucl. Sci. Technol. 7, 181–282 (1973)
McCourt, F.R.W., Beenakker, J.J.M., Köhler, W.E.E., Kušˇcer, I.: Nonequilibrium Phenomena in Polyatomic Gases Volume 2: Cross Sections, Scattering, and Rarefied Gases. Oxford University Press, Oxford (1991)
McDaniel, E.W., Mason, E.A.: The Mobility and Diffusion of Ions in Gases. Wiley, New York (1973)
McGuyer, B.H., Marslann III, R., Olsen, B.A., Happer, W.: Cusp kernels for velocity-changing collisions. Phys. Rev. Lett. 108, 183202 (2012)
McMahon, D.R.A., Shizgal, B.: Hot-electron zero-field mobility and diffusion in rare-gas moderators. Phys. Rev. A 31, 1894–1905 (1985)
McQuarrie, D.A., Simon, J.D.: Physical Chemistry: A Molecular Approach. University Science Books, California (1997)
Meijering, E.: A chronology of interpolation: from ancient astronomy to modern signal and image processing. Proc. IEEE 90, 319–342 (2002)
Meijering, E.H.W., Niessen, W.J., Viergever, M.A.: The Sinc-approximating kernels of classical polynomial interpolation. IEEE Int. Conf. Image Proc. 3, 652–656 (1999)
Meshkov, V.V., Stolyarov, A.V., Le Roy, R.J.: Adaptive analytical mapping procedure for efficiently solving the radial Schrödinger equation. Phys. Rev. A 78, 052510 (2008)
Messiah, A.: Quantum Mechanics, vol. I. North Holland, Amsterdam (1961)
Meyer, R.:Trigonometric interpolation method for one-dimensional quantum-mechanical problems. J. Chem. Phys. 52, 2053–2059 (1970)
Meyer-Vernet, N.: Large scale structure of planetary environments: the importance of not being Maxwellian. Planet. Space Sci. 49, 247–260 (2001)
Mielke, S.L., Chakraborty, A., Truhlar, D.G.: Vibrational configuration interaction using a tiered multimode scheme and tests of approximate treatments of vibrational angular momentum coupling: a case study for Methane. J. Phys. Chem. A 117, 7327–7343 (2013)
Miller, S.C., Good Jr, R.H.: A WKB-type approximation to the Schrödinger equation. Phys. Rev. 91, 174–179 (1953)
Milne, E.A.: Thermodynamics of the stars. Handbuch der Astrophysik 3, 65–255 (1930)
Milne, E.A.: Radiative equilibrium in the outer layers of a star; the temperature distribution and the law of darkening. Mon. Not. R. Astron. Soc. 81, 361–375 (1921)
Mintzer, D.: Generalized orthogonal polynomial solutions of the Boltzmann equation. Phys. Fluids 8, 1076–1090 (1965)
Mitani, M.: An application of double exponential formula to radial quadrature grid in density functional calculation. Theor. Chem. Acc. 130, 645–669 (2011)
Mitchner, M., Kruger, C.H.J.: Partially Ionized Gases. Wiley, New York (1973)
Moler, C.: Numerical Computing in MATLAB. SIAM, Philadelphia (2008)
Monchick, L., Mason, E.A.: Free flight theory of gas mixtures. Phys. Fluids 10, 1377–1390 (1967)
Montgomery, J.A., Chandler, D., Berne, B.J.: Trajectory analysis of a kinetic theory for isomerization dynamics in condensed phases. J. Chem. Phys. 70, 4056–4066 (1979)
Morgan, J.D.: Thomas-Fermi and other density—functional theories. In: Drake, G.W.F. (ed.) Atomic, Molecular and Optical Physics Handbook, pp. 233–242. AIP Press, New York (1996)
Morse, P.M.: Diatomic molecules according to the wave mechanics II. Vibrational levels. Phys. Rev. 34, 57–64 (1929)
Mott-Smith, H.M.: A new approach in the kinetic theory of gases. MIT Linc. Lab. V2, 1–1 (1954)
Mouhot, C.: Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation for hard potentials. Commun. Math. Phys. 261, 629–672 (2006)
Mouhot, C.: Quantitative linearized study of the Boltzmann collision operator and applications. Commun. Math. Sci. 1, 73–86 (2007)
Mozumder, A.: Electron thermalization in gases. III epithermal electron scavenging in rare gases. J. Chem. Phys. 74, 6911–6921 (1981)
Mozumder, A.: Fundamentals of Radiation Chemistry. Academic Press, London (1999)
Mullen,W.J., Laloë, F., Richards, M.G.: Longitudinal relaxation times for dilute quantum gases. J. Low Temp. Phys. 80, 1–13 (1990)
Müller, P.L.G., Hernandez, R., Benito, R.M., Borondo, F.: Detailed study of the direct numerical observation of the Kramers turnover in the LiNCLiCN isomerization rate. J. Chem. Phys. 137, 204301 (2012)
Müller-Plathe, F., Diercksen, G.H.F.: Molecular photoionization cross sections by moment theory. An introduction. In: Canuto, S., Castro, J.D., Paixao, F.J. (eds.) Electronic Structure of Atoms and Molecules, pp. 1–29. World Scientific, Singapore (1989)
Munn, R.J., Mason, E.A., Smith, F.J.: Some aspects of the quantal and semiclassical calculation of phase shifts and cross sections for molecular scattering and transport. J. Chem. Phys. 41, 3978–3988 (1964)
Mura, M.E., Knowles, P.J.: Improved radial grids for quadrature in molecular density-functional calculations. J. Chem. Phys. 104, 9848–9858 (1996)
Murray, C.W., Handy, N.C., Lamming, G.L.: Quadrature schemes for integrals of density functional theory. Mol. Phys. 78, 997–1014 (1993)


Nagel, B.: The relativistic Hermite polynomial is a Gegenbauer polynomial. J. Math. Phys. 35, 1549–1554 (1994)
Nakayama, T., Takahashi, K., Matsumi, Y.: Thermalization cross sections of suprathermal N(4S) atoms in collisions with atmospheric molecules. Geophys. Res. Lett. 32, L24803 (2005)
Nan, G., Houston, P.L.: Velocity relaxation of S(1D) by rare gases measured by Doppler spectroscopy. J. Chem. Phys. 97, 7865–7872 (1992)
Napier, D.G., Shizgal, B.D.: Sound dispersion in single-component systems. Physica A 387, 4099–4118 (2008)
Narayan, A., Klöckner, A.: deterministic numerical schemes for the Boltzmann equation, 1–51 (2009) ArXiv e-prints
Nauenberg, M.: Critique of q-entropy for thermal statistics. Phys. Rev. E 67, 036114 (2003)
Newbury, N.R., Barton, A.S., Cates, G.D., Happer,W., Middleton, H.: Gaseous 3He-3He magnetic dipolar relaxation. Phys. Rev. A 48, 4411–4420 (1993)
Newburgh, R., Peidle, J., Rueckner, W.: Einstein, Perrin, and the reality of atoms: 1905 revisited. Am. J. Phys. 74, 478–481 (2006)
Nicholson, D.R.: Introduction to Plasma Theory. Wiley, New York (1983)
Nicholson, J.W., Rudolph,W., Hager, G.: Using laser pulse dynamics to probe velocity distribution of excited iodine. J. Chem. Phys. 104, 3537–3545 (1996)
Nicolis, C.: Stochastic aspects of climatic transitions—response to a periodic forcing. Tellus 34, 1–9 (1982)
Nicolis, C., Nicolis, G.: Stochastic aspects of climatic transitions—additive fluctuations. Tellus 33, 225–234 (1981)
Nielsen, S.E., Bak, T.A.: Hard sphere model for the dissociation of diatomic molecules. J. Chem. Phys. 41, 665–674 (1964)
Noid, D.W., Marcus, R.A.: Semiclassical calculation of bound states in a multidimensional system for nearly 1:1 degenerate systems. J. Chem. Phys. 67, 559–567 (1977)
North, G.R.: Theory of energy-balance climate models. J. Atmos. Sci. 32, 2033–2043 (1975)


Oh, S.-K.: Modified Lennard-Jones potentials with a reduced temperature-correction parameter for calculating thermodynamic and transport properties: noble gases and their mixtures (He, Ne, Ar, Kr, and Xe). J. Thermodyn. 2013, 828620 (2013)
O’Hara, H., Smith, F.J.: Error estimation in the Clenshaw-Curtis quadrature formula. Comput. J. 11, 213–219 (1968)
Olmos, D.: Reflection and attachment of spirals at obstacles for the Fitzhugh-Nagumo and Beeler-Reuter models. Phys. Rev. E 81, 041924 (2010)
Olmos, D., Shizgal, B.D.: A pseudospectral method of solution of Fisher’s equation. J. Comput. Appl. Math 193, 219–242 (2006)
O’Neal, D., Neff, J.E.: OH 1.563μ absorption from starspots on active stars. Astron. J. 113, 1129–1137 (1997)
ONeil, S.V., Reinhardt,W.P.: Photoionization of molecular hydrogen. J. Chem. Phys. 69, 2126–2142 (1978)
Ordzywolek, A.: Gaussian integration with rescaling abscissas and weights. Comput. Phys. Commun. 182, 2533–2539 (2011)


Pack, R.T.: Space-fixed vs body-fixed axes in atom-diatomic molecule scattering. Sudden approximation. J. Chem. Phys. 60, 633–639 (1974)
Park, B.T., Petrosian, V.: Fokker-Planck equations of stochastic acceleration: a study of numerical methods. Astrophys. J. Suppl. Ser. 103, 225–267 (1996)
Park, J., Shafer, N., Bersohn, R.: The time evolution of the velocity distribution of hydrogen atoms in a bath gas. J. Chem. Phys. 91, 7861–7871 (1989)Parr, R.G.: Density functional theory. Annu. Rev. Phys. Chem. 34, 631–656 (1983)
Parker, E.N.: Dynamical theory of the solar wind. Space Sci. Rev. 4, 666–708 (1965)
Parker, E.N.: Kinetic and hydrodynamic representations of coronal expansion and the solar wind. AIP Conf. Proc. 1216, 3–7 (2010)
Parr, R.G.: Density functional theory. Annu. Rev. Phys. Chem. 34, 631–656 (1983)
Parr, R.G., Gosh, S.W.: Thomas-Fermi theory for atomic systems. Proc. Natl. Acad. Sci. 83, 3577–3579 (1986)
Parrish, R.M., Hohenstein, E.G., Martnez, T.J., Sherrill, C.D.: Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction. J. Chem. Phys. 138, 194107 (2013)
Pascal, S., Brun, R.: Transport properties of nonequilibrium gas mixtures. Phys. Rev. E 47, 3251–3267 (1993)
Pask, J.E., Sukumar, N., Monsavi, S.E.: Linear scaling solution of the all-electron Coulomb problem in solids. Int. J. Multiscale Comput. Eng. 10, 83–99 (2012)
Pasquetti, R., Rapetti, F.: Spectral element methods on triangles and quadrilaterals: comparisons and applications. J. Comput. Phys. 198, 349–362 (2004)
Pastor, R.W., Karplus, M.: Inertial effects in butane stochastic dynamics. J. Chem. Phys. 91, 211–218 (1989)
Pastore, P.: The numerical treatment of Love’s integral equation having a small parameter. J. Comput. Appl. Math. 236, 1267–1281 (2011)
Paul,W., Baschnagel, J.: Stochastic Processes; From Physics to Finance, 2nd edn. Springer, Berlin (2013)
Peeters, A.G., Strintzi, D.: The Fokker-Planck equation, and its application in plasma physics. Ann. Phys. (Berlin) 17, 142–157 (2008)
Pekeris, C.L.: Solution of the Boltzmann-Hilbert integral equation. Proc. Natl. Acad. Sci. 41, 661– 669 (1955)
Pekeris, C.L., Alterman, Z.: Solution of the Boltzmann-Hilbert integral equation II; the coefficients of viscosity and heat transfer. Proc. Natl. Acad. Sci. 43, 998–1007 (1957)
Peraiah, A.: Radiative transfer—Chandrasekhar—and after. Bull. Astron. Soc. India 24, 397–536 (1996)
Petrovay, K.: Solar cycle prediction. Living Rev. Sol. Phys. 7, 6–59 (2010)
Petrovi´c, Z.L., Dujko, S., Maric, D., Malovic, G., Nikitovic, Z., Sasic, O., Jovanovic, J.S.V., Radmilovic-Radenovic,M.: Measurement and interpretation of swarm parameters and their application in plasma modelling. J. Phys. D: Appl. Phys. 42, 194002 (2009)
Peyret, R.: Spectral Methods for Incompressible Viscous Flow. Springer, New York (2002)
Phillips, N.J.: Collisional relaxation in gases. Proc. Phys. Soc. 73, 800–806 (1959)
Pierrard, V.: Evaporation of hydrogen and helium atoms from the atmospheres of Earth and Mars. Planet. Space Sci. 51, 319–327 (2003)
Pierrard, V., Lemaire, J.: A collisional model of the polar wind. J. Geophys. Res. 103, 11701–11709 (1998)
Pierrard, V., Lazar, V.: Kappa distributions; theory and applications in space plasmas. Sol. Phys. 267, 153–174 (2010)
Pierrard, V., Lamy, H., Lemaire, J.: Exospheric distributions of minor ions in the solar wind.  J. Geophys. Res. 109, A02118 (2004)
Pindza, E., Patidar, K.C., Ngounda, E.: Robust spectral method for numerical valuation of European options under Merton’s jump-diffusion model. Numer. Methods Partial Differ. Equ. 30, 1169–1188 (2014)
Pinkus, A.: Weierstrass and approximation theory. J. Approx. Theory 107, 1–66 (2000)
Pitchford, L.C., ONeil, S.V., Rumble Jr, J.R.: Extended Boltzmann analysis of electron swarm experiments. Phys. Rev. A 23, 294–304 (1981)
Pitchford, L.C., Phelps, A.V.: Comparative calculations of electron-swarm properties in N2 at moderate E/N values. Phys. Rev. A 25, 540–554 (1982)
Planck,M.: Ueber einen satz der statistichen dynamik und eine erweiterung in der quantumtheorie. Sitzber. Preuß. Akad. Wiss. pp. 324–341 (1917)
Pollak, E., Talkner, P.: Reaction rate theory: what it was, where is it today, and where is it going?  Chaos 15, 026116 (2005)
Pollak, E., Ianconescu, R.: Finite barrier corrections to thePGHsolution of Kramers turnover theory. J. Chem. Phys. 140, 154108 (2014)
Pollak, E., Grabert, H., Hänggi, P.: Theory of activated rate processes for arbitrary frequency dependent friction: solution of the turnover problem. J. Chem. Phys. 91, 4073–4087 (1989)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)
Present, B.D., Morris, B.M.: Variational solution of the chemical kinetic Boltzmann equation. J. Chem. Phys. 50, 151–160 (1969)
Prandoni, P., Vetterli, M.: From Lagrange to Shanon. . . and back: another look at sampling. IEEE Signal Process. Mag. 26, 138–144 (2009)
Prenter, P.M.: Splines and Variational Methods. Wiley, New York (1975)
Press, W.H., Teukolsky, S.A., Veterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York (2007)
Prigogine, I., Xhrouet, E.: On the perturbation of Maxwell distribution function by chemical reactions in gases. Physica 15, 913–932 (1949)
Pryce, J.D.: Numerical Solution of Sturm-Liouville Problems. Oxford University Press, Oxford (1993)


Quarteroni, A., Saleri, F., Gervasio, P.: Scientific Computing with MATLAB and Octave, 3rd edn. Springer, New York (2010)


Rahman, M., Sundaresan, M.K.: Discrete relaxation modes for a hard sphere gas. Can. J. Phys. 46, 2463–2469 (1968)
Ralston, A., Rabinowitz, P.: A First Course in Numerical Analysis. Dover, New York (2001)
Rasch, J., Whelan, C.T.: On the numerical evaluation of a class of integrals occurring in scattering problems. Comput. Phys. Commun. 101, 31–46 (1997)
Reed, W. H., Hill T.R.: Triangular Mesh Methods for the Neutron Transport Equation. Technical
Report LA-UR-73-479, Los Alamos Scientific Laboratory (1973)
Reif, F.: Fundamentals of Statistical and Thermal Physics. Waveland Press, Illinois (2008)
Reine, S., Helgaker, T., Lindh, R.: Multi-electron integrals. WIREs Comput. Mol. Sci. 2, 290–303 (2012)
Reinhardt,W.P.: L2 discretization of atomic and molecular electronic continua: moment, quadrature and J-matrix techniques. Comput. Phys. Commun. 17, 1–21 (1979)
Risken, H.: The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edn. Springer, Berlin (1996)
Risken, H., Till, F.: The Fokker-Planck equation: Methods of solution and applications, 2nd edn. Springer, Berlin (1996)
Risken, H., Voigtlaender, K.: Solutions of the Fokker-Planck equation describing thermalization of neutrons in a heavy gas moderator. Z. Phys. B—Condens. Matter 54, 253–262 (1984)
Rivlin, T.J.: An Introduction to the Approximation of Functions. Blaisdell Publishing Co., Toronto (1969)
Robson, R.E.: Introductory Transport Theory for Charges Particles in Gases. World Scientific, Singapore (2006)
Robson, R.E., White, R.D., Petrovi´c, Z.L.: Colloquium: physically based fluid modeling of collisionally dominated low-temperature plasmas. Rev. Mod. Phys. 77, 1303–1320 (2005)
Robson, R.E., Ness, K.F., Sneddon, G.E.,Viehland, L.A.: Comment on the discrete ordinate method in the kinetic theory of gases. J. Comput. Phys. 92, 213–229 (1991)
Robson, R.E., Prytz, A.: A discrete ordinate pseudo-spectral method: review and application from a physicist’s perspective. Aust. J. Phys. 46, 465–495 (1993)
Robson, R.E., Ness, K.F.: Velocity distribution and transport coefficients of electron swarms in gases: spherical-harmonic decomposition of Boltzmann’s equation. Phys. Rev. A 33, 2068–2077 (1986)
Rosenbluth, M., Macdonald, F.W.M., Judd, D.L.: Fokker-Planck equation for an inverse-square force. Phys. Rev. 107, 1–6 (1957)
Ross, J., Mazur, P.: Some deductions from a formal statistical mechanical theory of chemical kinetics. J. Chem. Phys. 35, 19–28 (1961)
Russo, G., Smereka, P.: The Gaussian wave packet transform: efficient computation of the semiclassical limit of the Schrödinger equation. Part 1. Formulation and the one dimensional case. J. Comput. Phys. 233, 192–209 (2013)
Russo, G., Smereka, P.: The Gaussian wave packet transform: efficient computation of the semiclassical limit of the Schrödinger equation. Part 2. Multidimensional case. J. Comput. Phys. 257, 1022–1038 (2014)
Rybicki, G.B., Lightman, A.P.: Radiative Processes in Astrophysics.Wiley Interscience, New York (1979)
Rybicki, G.B.: Radiative transfer. J. Astrophys. Astron. 17, 95–112 (1996)
Ryckaert, J.-P., Bellemans, A.: Molecule dynamics of liquid alkanes. Faraday Discuss. Chem. Soc. 66, 95–106 (1978)
Rys, J., Dupuis, M., King, H.F.: Computation of electron repulsion integrals using Rys quadrature method. J. Comput. Chem. 4, 154–175 (1983)


Sabbane,M., Tij, M., Santos, A.:Maxwellian gas undergoing a stationary Poiseuille flow in a pipe. Physica A 327, 264–290 (2003)
Safouhi, H.: The properties of sine, spherical Bessel and reduced Bessel functions for improving convergence of semi-infinite very oscillatory integrals: the evaluation of three-centre nuclear attraction integrals over B-functions. J. Phys. A: Math. Gen. 34, 2801–2818 (2001)
Sack, R.A., Donavan, A.F.: An algorithm for Gaussian quadrature given modified moments. Numer. Math. 18, 465–478 (1972)
Sagar, P.R., Smith, V.H.: On the calculation of Rys polynomials and quadratures. Int. J. Quant. Chem. 42, 827–836 (1992)
Sakai, Y.: Quasifree electron transport under electric field in nonpolar simple-structured condensed matters. J. Phys. D: Appl. Phys. 40, R441–R452 (2007)
Sandberg, J.A.R., Rinkevicius, Z.:An algorithm for the efficient evaluation of two-electron repulsion integrals over contracted Gaussian-type basis functions. J. Chem. Phys. 137, 234105 (2012)
Santos, A.: Solutions of the moment hierarchy in the kinetic theory of Maxwell models. Contin. Mech. Thermodyn. 21, 361–387 (2009)
Sarkar, T.K.: A note on the variational method (Rayleigh-Ritz), Galerkin’s methods and the method of weighted residuals. Radio Sci. 18, 1207–1224 (1983)
Schenzle, A., Brand, H.: Multiplicative stochastic processes in statistical physics. Phys. Rev. A 20, 1628–1647 (1979)
Schindler, M., Talkner, P., Hänggi, P.: Escape rates in periodically driven Markov processes. Physica A 351, 40–50 (2005)
Schneider, B.I., Nygaard, N.: Orthogonal functions, discrete variable representation and generalized Gauss quadratures. J. Phys. Chem. A 106, 10773–10776 (2002)
Schulz, M., Lanzerotti, M.L.: Particle Diffusion in the Radiation Belts. Springer, Berlin (1974)
Schumer, J.W., Holloway, J.P.: Vlasov simulations using velocity-scaled Hermite representations. J. Comput. Phys. 144, 626–661 (1998)
Schunk, R.W.: Mathematical structure of transport equations for multispecies flows. Rev. Geophys. Space Phys. 15, 429–445 (1977)
Schwartz, C.: High-accuracy approximation techniques for analytic functions. J. Math. Phys. 26, 411–415 (1985)
Scudder, J.D.: Ion and electron suprethermal tail strengths in the transition region for the velocity filtration model of the corona. Astrophys. J. 427, 446–452 (1994)
Secrest, D., Johnson, B.R.: Exact quantum-mechanical calculation of a collinear collision of a particle with a harmonic oscillator. J. Chem. Phys. 45, 4556–4570 (1966)
Seinfeld, J.H., Pandis, S.N.: Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd edn. Wiley, New York (2006)
Shapiro, D.A.: Spectral line narrowing in the Keilson-Storer model. J. Phys. B: At. Mol. Opt. Phys. 33, L43–L49 (2000)
Sharipov, F., Seleznev, V.: Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27, 657–706 (1998)
Sharipov, F., Bertoldo, G.: Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential. J. Comput. Phys. 228, 3345–3357 (2009)
Shavitt, I., Karplus, M.: Gaussian-transform method for molecular integrals. I. Formulation of energy integrals. J. Chem. Phys. 43, 398–414 (1965)
Shematovich, V.I., Bisikalo, D.V., Gérard, J.-C., Cox, C., Bougher, S.W.: Monte Carlo model of electron transport for the calculation of mars dayglow emissions. J. Geophys. Res. 113, E02011 (2008)
Shen, J., Yu, H.: Efficient spectral sparse grid methods and applications to high dimensional elliptic equations II. Unbounded domains. SIAM J. Sci. Comput. 34, A1141–A1164 (2012)
Shen, J., Tang, T.,Wang, L.-L.: Spectral Methods: Algorithms Analysis and Applications. Springer, Berlin (2011)
Sherrill, C.D.: Frontiers in electronic structure theory. J. Chem. Phys. 132, 110902 (2010)
Shizgal, B.D.: Pseudospectral methods of solution of the linear and linearized Boltzmann equations; transport and relaxation. AIP Conf. Proc. 1333, 986–991 (2011)
Shizgal, B.D.: Suprathermal particle distributions in space physics: kappa distributions and entropy. Astrophys. Space Sci. 312, 227–237 (2007)
Shizgal, B.D.: Coulomb collisional processes in space plasmas; relaxation of suprathermal particle distributions. Planet. Space Sci. 52, 923–933 (2004)
Shizgal, B.D.: Spectral methods based on nonclassical basis functions: the advection-diffusion equation. Comput. Fluids 31, 825–843 (2002)
Shizgal, B.D.: An analysis of O-H interaction potentials, O-H and O-D cross sections and vibrational states. Planet. Space Sci. 47, 163-174 (1999)
Shizgal, B.D.: The quadrature discretization method (QDM) in the calculation of the rotationalvibrational transitions in rare gas dimers. J. Mol. Struct. (Theochem) 391,
131–139 (1997)
Shizgal, B.: Spectral theory and the approach to equilibrium in a plasma. Trans. Theory Stat. Phys. 21, 645–665 (1992)
Shizgal, B.: Relaxation in ionized gases: the role of the spectrum of the collision operator. In: Beylich, A.E. (ed.) Proceedings of the 17th International Symposium on Rarefied Gas Dynamics, pp. 22–29. VCH Verlagsgesellschaft GmbH, Berlin (1991)
Shizgal, B.: Negative differential conductivity of electrons in He-Xe and He-Kr mixtures. Chem. Phys. 147, 271–279 (1990)
Shizgal, B.: The coupling of electron thermalisation and electron attachment; SF6 and CC14 in rare-gas moderators. J. Phys. B: At. Mol. Opt. Phys. 21, 1699–1715 (1988)
Shizgal, B.: Electron distribution functions for electron attachment to SF6 and model systems. Chem. Phys. Lett. 138, 65–70 (1987)
Shizgal, B.: Discrete versus continuum relaxation modes of a hard sphere gas. Can. J. Phys. 62, 97–103 (1984)
Shizgal, B.: Nonequilibrium time dependent theory of hot atom reactions. III. Comparison with the Estrup-Wolfgang theory. J. Chem. Phys. 74, 1401–1408 (1981)
Shizgal, B.: A Gaussian quadrature procedure for the use in the solution of the Boltzmann equation and related problems. J. Comput. Phys. 41, 309–328 (1981)
Shizgal, B.: Eigenvalues of the Lorentz Fokker-Planck equation. J. Chem. Phys. 70, 1948–1951 (1979)
Shizgal, B.: Calculation of the NMR relaxation time for dilute 129Xe gas. Chem. Phys. 5, 464–470 (1974)
Shizgal, B.: A method for the rapid calculation of matrix elements with highly oscillatory JWKB radial wavefunctions. Chem. Phys. Lett. 24, 369–372 (1974)
Shizgal, B.: Time dependent solution of the chemical kinetic Boltzmann equation; two component isothermal system. Chem. Phys. 5, 129–135 (1974)
Shizgal, B.: Kinetic theory calculation of NMR relaxation time for dilute 3He gas. J. Chem. Phys. 58, 3424–3431 (1973)
Shizgal, B.: Vibrational nonequilibrium effects in the (H2-H2) reactive system. J. Chem. Phys. 57, 3915–3928 (1972)
Shizgal, B.: Nonequilibrium contributions to the rate of reaction. IV. Explicit time-dependent solutions. J. Chem. Phys. 55, 76–83 (1971)
Shizgal, B.D., Arkos, G.G.: Nonthermal escape of the atmospheres of Venus, Earth, and Mars. Rev. Geophys. 34, 483–505 (1996)
Shizgal, B., Barrett, J.C.: Time dependent nucleation. J. Chem. Phys. 91, 6505–6518 (1989)
Shizgal, B., Blackmore, R.: Eigenvalues of the Boltzmann collision operator for binary gases and relaxation of anisotropic distributions. Chem. Phys. 77, 417–427 (1983)
Shizgal, B., Blackmore, R.: A discrete ordinate method of solution of linear boundary value and eigenvalue problems. J. Comput. Phys. 55, 313–327 (1984)
Shizgal, B., Blackmore, R.: A collisional kinetic theory of a plane parallel evaporating planetary atmosphere. Planet. Space Sci. 34, 279–291 (1986)
Shizgal, B.D., Chen, H.: The quadrature discretization method (QDM) in the solution of the Schrödinger equation with nonclassical basis functions. J. Chem. Phys. 104, 4137–4150 (1996)
Shizgal, B.D., Chen, H.: The quadrature discretization method in the solution of the Fokker-Planck equation with nonclassical basis functions. J. Chem. Phys. 107, 8051–8063 (1997)
Shizgal, B.D., Dridi, R.: Maple code for the calculation of the matrix elements of the Boltzmann collision operators for mixtures. Comput. Phys. Commun. 181, 1633–1640 (2010)
Shizgal, B., Fitzpatrick, J.M.: Matrix elements of the linear Boltzmann collision operator for systems of two components at different temperatures. Chem. Phys. 6, 54–65 (1974)
Shizgal, B., Fitzpatrick, J.M.: Possible failure of relaxation-time comparisons in the justification of local thermodynamic equilibrium. Phys. Rev. A 18, 267–276 (1978)
Shizgal, B., McMahon, D.R.A.: Electric field dependence of transient electron transport properties in rare gas moderators. Phys. Rev. A 32, 3669–3680 (1985)
Shizgal, B., Hubert, D.: The nonequilibrium nature of ion distribution functions in the high latitude auroral ionosphere. In: Muntz, E.P.,Weaver, D.P., Campbell, D.H. (eds.) Proceedings of the 16th International Symposium on Rarefied Gas Dynamics, pp. 3–22. AIAA, Washington (1989)
Shizgal, B.D., Jung, J.-H.: Towards the resolution of the Gibbs phenomena. J. Comput. Appl. Math. 161, 41–65 (2003)
Shizgal, B., Karplus, M.: Nonequilibrium contributions to the rate of reaction. I. Perturbation of the velocity distribution function. J. Chem. Phys. 52, 4262–4278 (1970)
Shizgal, B., Karplus, M.: Nonequilibrium contributions to the rate of reaction. II. Isolated multicomponent systems. J. Chem. Phys. 54, 4345–4356 (1971)
Shizgal, B., Lindenfeld, M.J.: Energy distribution function of translationally hot O(3P) atoms in the atmosphere of earth. Planet. Space Sci. 27, 1321–1332 (1979)
Shizgal, B.D., Lordet, F.: Vibrational nonequilibrium in a supersonic expansion with reaction: application to O2-O. J. Chem. Phys. 104, 3579–3597 (1996)
Shizgal, B., McMahon, D.R.A.: Electric field dependence of transient electron transport properties in rare gas moderators. Phys. Rev. A 32, 3669–3680 (1985)
Shizgal, B., McMahon, D.R.A., Viehland, L.A.: Thermalization of electrons in gases. Radiat. Phys. Chem. 34, 35–50 (1989)
Shizgal, B.D., Napier, D.G.: Nonequilibrium effects in reactive systems: the effect of reaction products and the validity of the Chapman-Enskog method. Physica A 223, 50–86 (1996)
Shizgal, B., Ness, K.: Thermalisation and annihilation of positrons in helium and neon. J. Phys. B: At. Mol. Phys. 20, 847–865 (1987)
Shizgal, B., Weinert, U., Blackmore, R.: The QDM in the solution of the Kramers equation for symmetrical potentials. In: Beylich, A.E. (ed.) Proceedings of the 17th International Symposium on Rarefied Gas Dynamics, pp. 85–92. Wiley, Weinheim (1991)
Shohat, J.A., Tamarkin, J.D.: The Problem of Moments. American Mathematical Society, NewYork (1943)
Shore, B.W.: B-spline expansion bases for excited states and discretized scattering states. J. Chem. Phys. 63, 3835–3840 (1975)
Shore, B.W.: Solving the radial Schrödinger equation by using cubic-spline basis functions. J. Chem. Phys. 58, 3855–3866 (1973)
Shore, S.N.: Blue sky and hot piles: the evolution of radiative transfer theory from atmospheres to nuclear reactors. Hist. Math. 29, 463–489 (2002)
Shoub, E.C.: Failure of the Fokker-Planck approximation to the Boltzmann integral for 1/r potentials. Phys. Fluids 30, 1340–1352 (1987)
Shu, C.: Differential Quadrature and Its Application in Engineering. Springer, Berlin (2000)
Shu, C., Ding, H.,Yeo, K.S.: Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 192, 941–954 (2003)
Siewert, C.E.: A concise and accurate solution to Chandrasekhar’s basic problem in radiative transfer. JQRST 64, 109–130 (2000)
Siewert, C.E.: On computing the Chapman-Enskog functions for viscosity and heat transfer and the Burnett functions. JQRST 74, 789–796 (2002)
Siewert, C.E.: The linearized Boltzmann equation: concise and accurate solutions to basic flow problems. Z. angew. Math. Phys. 54, 273–303 (2003)
Singh, G.S., Prasad, N., Kumar, B.: Transport properties of a binary gas mixture of molecules with internal energy. II. Thermal conductivity. J. Chem. Phys. 105, 1537–1545 (1996)
Skinner, J,l, Wolynes, P.G.: General kinetic models of activated processes in condensed phases. J. Chem. Phys. 72, 4913–4927 (1980)
Slevinsky, M., Safouhi, H.: Numerical treatment of a twisted tail using extrapolation methods. Numer. Algorithms 48, 301–316 (2008)
Snider, R.F.: Quantum-mechanical modified Boltzmann equation for degenerate internal states. J. Chem. Phys. 32, 1051–1060 (1960)
Snider, R.F.: Variational methods for solving the Boltzmann equation. J. Chem. Phys. 41, 591–595 (1964)
Solomon, S.C.: Auroral particle transport using Monte Carlo and hybrid methods. J. Geophys. Res. 106, 107–116 (2001)
Sone, Y.: Molecular Gas Dynamics: Theory, Techniques and Applications. Birkhauser, Boston (2007)
Sospedra-Alfonso, R., Shizgal, B.D.: Kullback-Leibler entropy in the electron distribution shape relaxation for electron-atom thermalization. Phys. Rev. E 84, 041202 (2011)
Sospedra-Alfonso, R., Shizgal, B.D.: Henyey-Greenstein model in the shape relaxation of dilute gas mixtures. Trans. Theory Stat. Phys. 41, 368–388 (2012)
Sospedra-Alfonso, R., Shizgal, B.D.: Hot atom populations in the terrestrial atmosphere. A comparison of the nonlinear and linearized Boltzmann equation. AIP Conf. Proc. 1501, 91–98 (2012)
Sospedra-Alfonso, R., Shizgal, B.D.: Energy and shape relaxation in binary atomic systems with realistic quantum cross sections. J. Chem. Phys. 139, 044113 (2013)
Spendier, K., Sugaya, S., Kenkre, V.M.: Reaction-diffusion theory in the presence of an attractive harmonic potential. Phys. Rev. E 88, 062142 (2013)
Spitzer, L.J.: Physics of Fully Ionized Gases. Interscience, New York (1962)
Spitzer, L.J.: Physical Processes in the Interstellar Medium. Wiley, New York (1998)
Spitzer, L.J., Härm, R.: Evaporation of stars from open clusters. Astrophys. J. 127, 544–550 (1958)
St.-Maurice, J.-P., Schunk, R.W.: Behaviour of ion velocity distributions for a simple collision model. Planet. Space Sci. 22, 1–18 (1974)
St.-Maurice, J.-P., Schunk,R.W.: Use of generalized orthogonal polynomial solutions of Boltzmanns equation in certain aeronomy problems, Auroral ion velocity distributions. J. Geophys. Res. 81, 2145–2154 (1976)
St.-Maurice, J.-P., Schunk, R.W.: Ion velocity distributions in the high-latitude ionosphere. Rev. Geophys. 17, 99–134 (1979)
Stamnes, K.: Analytic approach to auroral electron transport and energy degradation. Planet. Space Sci. 28, 427–441 (1980)
Stamnes, K., Tsay, S.-C.,Wiscombe,W., Jayaweera, K.: Numerically stable algorithm for discreteordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt. 27, 2502–2509 (1988)
Stare, J., Balint-Kurti, G.G.: Fourier grid Hamiltonian method for solving the vibrational Schrödinger equation in internal coordinates: theory and test applications. J. Phys. Chem. A 107, 7204–7214 (2003)
Steen, N.M., Byrne, G.D., Gelbard, E.M.: Gaussian quadratures for the integrals  ∞ 0 exp(−x2) f (x)dx and  b 0 exp(−x2) f (x)dx. Math. Comput. 23, 661–671 (1969)
Stefan, W., Viswanathan, A., Gelb, A., Renaut, R.: Sparsity enforcing edge detection method for blurred and noisy Fourier data. J. Sci. Comput. 50, 536–556 (2012)
Steffens, K.G.: The History of Approximation Theory: From Euler to Bernstein. Birkhäuser, Boston (2006)
Stenger, F.: Numerical methods based on Sinc and analytic functions. Springer Series in Comp. Math. 20, 91–96 (1993)
Stix, T.H.: Waves in Plasmas. Springer, New York (1992)
Stroud, A.H.: Approximate Calculation of Multiple Integrals. Prentice Hall, Engelwood Cliffs (1971)
Stroud, A.H., Secrest, D.: Gaussian Quadrature Formulas. Prentice-Hall, New Jersey (1966)
Struchtrup, H.: Macroscopic Transport Equations for Rarefied Gas Flows; Approximation Methods in Kinetic Theory. Springer, New York (2005)
Sturgill, D.: Variable shape parameter strategies in radial basis function methods. Ph.D. thesis, Marshall University, West Virginia, USA (2009) (Sturgill (Thesis) – 2009)
Sykes, J.B.: Approximate integration of the equation of transfer. Mon. Not. R. Astron. Soc. 111, 377–386 (1951)
Szabo, A., Schulten, K., Schulten, Z.: First passage time approach to diffusion controlled reactions. J. Chem. Phys. 72, 4350–4357 (1980)
Szabo, A., Ostlund, N.S.: Modern Quantum Chemistry, Introduction to Advanced Electronic Structure Theory. Dover, New York (1996)
Szalay,V.: Discrete variable representations of differential operators. J. Chem. Phys. 99, 1978–1984 (1993)
Szalay, V., Szidarovsky, T., Czakó, G., Császár, A.G.: A paradox of grid-based representation techniques: accurate eigenvalues from inaccurate matrix elements. J. Math. Chem. 50, 636–651 (2012)
Szalay, V., Czakó, G., Nagy, A., Furtenbacher, T., Császár, A.G.: On one-dimensional discrete variable representations with general basis functions. J. Chem. Phys. 119, 10512–10518 (2003)


Taatjes, C.A., Cline, J.I., Leone, S.R.: A general method for Doppler determination of cylindrically symmetric velocity distributions: an application of Fourier transform Doppler spectroscopy. J. Chem. Phys. 93, 6554–6559 (1990)
Tadmor, E., Tanner, J.: Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information. Found. Comput. Math. 2, 155–189 (2002)
Talman, L.A.: Simpson’s rule is exact for quintics. Am. Math. Mon. 113, 144–155 (2006)
Tang, T.: The Hermite spectral method for Gaussian-type functions. SIAM J. Sci. Comput. 14, 594–606 (1993)
Tang, K.T., Toennies, J.P.: The van der Waals potentials between all the rare gas atoms from He to Rn. J. Chem. Phys. 118, 4976–4983 (2003)
Tangman, D.Y., Gopaul, A., Bhuruth, M.: Exponential time integration and Chebyshev discretisation schemes for fast pricing of options. Appl. Numer. Math. 58, 1309–1319 (2008)
Tatari, M., Haghighi, M.: A generalized Laguerre-Legendre spectral collocation method for solving initial-boundary value problems. Appl. Math. Model. 38, 1351–1364 (2014)
Taylor, J.R.: Scattering Theory: The Quantum Theory on Nonrelativistic Collisions. Dover, New York (2012)
Thévenaz, P.: Interpolation revisited. IEEE Trans. Med. Imaging 19, 739–758 (2000)
Thomas, L.H.: The calculation of atomic fields. Proc. Camb. Philos. Soc. 23, 542–548 (1927)
Thomas, G.E., Stamnes, K.: RadiativeTransfer in the Atmosphere and Ocean. Cambridge University Press, Cambridge (2002)
Tomaschitz, R.: Multipole fine structure of the cosmic microwave background: reconstruction of the temperature power spectrum. Mon. Not. R. Astron. Soc. 427, 1363–1383 (2012)
Tomaschitz, R.: Bessel integrals in epsilon expansion: squared spherical Bessel functions averaged with Gaussian power-law distributions. Appl. Math. Comput. 225, 228–241 (2013)
Tompson, R.V., Tipton, E.L., Loyalka, S.K.: Chapman-Enskog solutions to arbitrary order in Sonine polynomials V: summational expressions for the viscosity-related bracket integrals. Eur. J. Mech. B/Fluids 29, 153–179 (2010)
Trahan, C.J., Wyatt, R.E.: Radial basis function interpolation in the quantum trajectory method: optimization of the multi-quadric shape parameter. J. Comput. Phys. 185, 27–49 (2003)
Travis, K.P., Searles, D.J.: Effect of solvation and confinement on the trans-gauche isomerization reaction in n-butane. J. Chem. Phys. 125, 164501 (2006)
Trefethen, L.N.: Approximation Theory and Approximation Practice. SIAM, Philadelphia (2013)
Trefethen, L.N.: Is Gauss quadrature better than Clenshaw-Curtis? SIAM Rev. 50, 67–87 (2008)
Trefethen, L.N.: Spectral Methods in MATLAB. SIAM, Philadelphia (2000)
Treumann, R.A., Jaroschek, C.H., Scholer, M.: Stationary plasma states far from equilibrium. Phys. Plasmas 11, 1317–1325 (2004)
Treutler, O., Ahlrichs, R.: Efficient molecular numerical integration schemes. J. Chem. Phys. 102, 346–354 (1995)
Tricomi, F.G.: Integral Equations. Dover, New York (1985)
Truhlar, D.G., Wyatt, R.E.: History of H3 kinetics. Annu. Rev. Phys. Chem. 27, 1–43 (1976)
Trunec, D., Španˇel, P., Smith, D.: The influence of electron-electron collisions on electron thermalization in He and Ar afterglow plasmas. Chem. Phys. Lett. 372, 728–732 (2003)
Tsallis, C.: Non-extensive thermostatics: brief review and comments. Physica A 221, 277–290 (1995)
Tsallis, C.: Comment on Critique of q-entropy for thermal statistics. Phys. Rev. E 69, 038101 (2004)
Tsuneda, T.: Density Functional Theory in Quantum Chemistry. Springer, New York (2014)


Ueda, M., Sargeant, A.J., Pato, M.P., Hussein, M.S.: Effective astrophysical S factor for nonresonant reactions. Phys. Rev. C 61, 045801 (2000)
Uhlenbeck, G.E., Ornstein, L.S.: On the theory of the Brownian motion. Phys. Rev. 36, 823–841 (1930)


Vasenkov, A., Shizgal, B.D.: Nonhydrodynamic aspects of electron transport near a boundary: the Milne problem. Phys. Rev. E 63, 016401 (2000)
Vasenkov, A., Shizgal, B.D.: Numerical study of a direct current plasma sheath based on kinetic theory. Phys. Plasmas 9, 691–700 (2002)
Ven Den Eynde, G., Beauwens, R., Mund, E.: Calculating the discrete spectrum of the transport operator with arbitrary order anisotropic scattering. Trans. Theory Stat. Phys. 36, 179–197 (2007)
van Kampen, N.G.: Stochastic Processes in Physics and Chemistry, 3rd edn. North Holland, Amsterdam (2007)
Viehland, L.A.: Velocity distribution functions and transport coefficients of atomic ions in atomic gases by a Gram-Charlier approach. Chem. Phys. 179, 71–92 (1994)
Viehland, L.A., Chang, Y.: Beyond the Monchick-Mason approximation: the mobility of Li ions in H2. Mol. Phys. 110, 259–266 (2012)
Viehland, L.A., Lin, S.L.: Application of the three temperature theory of ion transport. Chem. Phys. 43, 135–144 (1979)
Viehland, L.A., Ranganathan, B., Shizgal, S.: Transient microwave conductivity of electrons in helium and argon. J. Chem. Phys. 88, 362–370 (1988)
Vocks, C.: A kinetic model for ions in the solar corona including wave-particle interactions and Coulomb collisions. Astrophys. J. 568, 1017–1029 (2002)
Voigtlaender, K., Risken, H.: Solutions of the Fokker-Planck equation for a double-well potential in terms of continued fractions. J. Stat. Phys. 40, 397–429 (1985)
Volakis, J., Sertel, K.: Integral Equation Methods for Electromagnetics. Scitech, North Carolina (2012)
Vozovoi, L.,Weill, A., Israeli, M.: Spectrally accurate solution of nonperiodic differential equations by the Fourier-Gegenbauer method. SIAM J. Numer. Anal. 34, 1451–1471 (1997)


Waldvogel, J.: Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT Numer. Math. 46, 195–202 (2006)
Wang, H., Xiang, S.: On the convergence rates of Legendre approximation. Math. Comput. 81, 861–877 (2012)
Wang-Chang, C.S., Uhlenbeck G.S.: Solution of the transport equation by SN approximation. Technical Report CM-681, University of Michigan (1951)
Wannier, G.H.: Derivation of the Davydov distribution from the Boltzmann equation. Am. J. Phys. 39, 281–285 (1971)
Warringa, H.J., Sedrakian, A.: Vortex formation in a rotating two-component Fermi gas. Phys. Rev. A 84, 023609 (2011)
Wei, H.: Ghost levels and near-variational forms of the discrete variable representation: application to H2O. J. Chem. Phys. 106, 6885–6900 (1997)
Wei, G.W.: Discrete singular convolution for the solution of the Fokker Planck equation. J. Chem. Phys. 110, 8930–8942 (1999)
Wei, G.W.: Solving quantum eigenvalue problems by discrete singular convolution. J. Phys. B: At. Mol. Opt. Phys. 33, 343–352 (2000)
Wei, G.W.: Wavelets generated by using discrete singular convolution kernels. J. Phys. A: Math. Gen. 33, 8577–8596 (2000)
Wei, G.W., Zhang, D.S., Kouri, D.J., Hoffman, D.K.: Lagrange distributed approximating functionals. Phys. Rev. Lett. 79, 775–779 (1997)
Weideman,W.A.C.: Spectral methods based on non-classical polynomials. In: Gautschi, G., Golub, G.H., Opfer, G. (eds.) Approximations and Computation of Orthogonal Polynomials, pp. 239–251. birkhauser, Basel (1999)
Weideman, J.A.C., Reddy, S.C.: A MATLAB differentiation matrix suite. ACM Trans.Math. Softw. 26, 465–519 (2000)
Weinert, U., Lin, S.L., Mason, E.A.: Solutions of the nonlinear Boltzmann equation describing relaxation to equilibrium. Phys. Rev. A 22, 2262–2269 (1980)
Weniger, E.J.: On the analyticity of Laguerre series. J. Phys. A: Math. Theor. 41, 425207 (2008)
Weniger, E.J.: The strange history of B functions or how theoretical chemists and mathematicians do (not) interact. Int. J. Quant. Chem. 109, 1706–1716 (2009)
Wheeler, J.C.: Modified moments and Gaussian quadratures. Rocky Mt. J.Math. 4, 287–296 (1974)
Wilbraham, H.: On certain periodic functions. Camb. Dublin Math. J. 3, 198–201 (1848)
Williams, P.: Quadrature discretization method in tethered satellite control. Appl. Math. Comput. 217, 8223–8235 (2011)
Whittaker, J.M.: The Fourier theory of the Cardinal function. Proc. Roy. Soc. Edinb. 1, 169–176 (1929a)
Whittaker, J.M.: On the Cardinal function of interpolation theory. Proc. Roy. Soc. Edinb. 1, 41–46 (1929b)
White, R.D., Dujko, S., Robson, R.E., Petrovi´c, Z.L., McEachran, R.P.: Non-equilibrium transport of positron and electron swarms in gases and liquids. Plasma Sources Sci. Technol. 19, 034001 (2010)
White, R.D., Robson, R.E.: Multiterm solution of a generalized Boltzmann kinetic equation for electron and positron transport in structured and soft condensed matter. Phys. Rev. E 84, 031125 (2011)
Wick, G.C.: Über ebene diffusionsprobleme. Z. Phys. 121, 702–718 (1943)
Wigner, E.P.:Asolution of Boltzmann’s equation for monoenergetic neutrons in an infinite medium. Technical Report AECD-3125, U.S. Atomic Energy Commission (1943)
Wigner, E.P., Wilkins Jr, J.E.: Effect of temperature of the moderator on the velocity distribution of neutrons with numerical calculations for H as moderator. Technical Report AECD-2275, U.S. Atomic Energy Commission (1944)
Wilkinson, M., Pumir, A.: Spherical Ornstein-Uhlenbeck process. J. Stat. Phys. 145, 113–142 (2011)
Williams, M.M.R.: The Slowing Down and Thermalization of Neutrons. North-Holland, Amsterdam (1966)
Williams, M.M.R.: Mathematical Methods in Particle Transport Theory. Wiley-Interscience, New York (1971)
Williams, M.M.R.: The Boltzmann equation for fast atoms. J. Phys. A: Math. Gen. 9, 771–783 (1976)
Williams, M.M.R.: The development of nuclear reactor theory in the Montreal laboratory of the National Research Council of Canada (Division of Atomic Energy) 1943–1946. Prog. Nucl. Energy 36, 239–322 (2000)
Williams, M.M.R.: The Milne problem with Fresnel reflection. J. Phys. A: Math. Gen. 38, 3841–3850 (2005)
Williams, P.: Quadrature discretization method in tethered satellite control. Appl. Math. Comput. 217, 8223–8235 (2011)
Willner, K., Dulieu, O., Masnou-Seeuws, F.: Mapped grid methods for long-range molecules and cold collisions. J. Chem. Phys. 120, 548–561 (2004)
Wind, H.: Electron energy for H+2 in the ground state. J. Chem. Phys. 42, 2371–2373 (1965)
Wright, J.S., Donaldson, D.J.: Potential energy and vibrational levels for local modes in water and acetylene. Chem. Phys. 94, 15–23 (1985)
Wu, L., White, C., Scanlon, T.J., Reese, J.M., Zhang, Y.: Deterministic numerical solutions of the Boltzmann equation using the fast spectral method. J. Comput. Phys. 250, 27–52 (2013)


Xiang, S.: Asymptotics on Laguerre or Hermite polynomial expansions and their applications in Gauss quadrature. J. Math. Anal. Appl. 393, 434–444 (2012)

Yan, C.C.: Relaxation rate spectrum of the linearized Boltzmann equation for hard spheres. Phys. Fluids 12, 2306–2312 (1969)
Yang, W., Peet, A.C.: The collocation method for bound solutions of the Schrödinger equation. Chem. Phys. Lett. 153, 98–104 (1988)
Yilmazer, A., Kocar, C.: Some benchmark results in spherical media radiative transfer problems. Trans. Theory Stat. Phys. 38, 273–292 (2009)


Zhao, S., Wei, G.W.: Comparison of the discrete singular convolution and three other numerical schemes for solving Fisher’s equation. SIAM J. Sci. Comput. 25, 127–147 (2003)
Zhang, P., Kharchenko, V., Dalgarno, A.: Thermalization of suprathermal N(4S) atoms in He and Ar gases. Mol. Phys. 105, 1487–1496 (2007)
Zhang, X.-N., Li, H.-P., Murphy, A.B., Xia,W.-D.: A numerical model of non-equilibrium thermal plasmas. I. Transport properties. Phys. Plasmas 20, 033508 (2013)
Ziff, R.M., Merajver, S.D., Stell, G.: Approach to equilibrium of a Boltzmann-equation solution. Phys. Rev. Lett. 47, 1493–1496 (1981)