Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker–Planck Equations

Boyd, J.P.: The rate of convergence of Hermite function series. Math. Comput. 35, 1309–1316 (1980)

Carrillo, J.A., Rosado, J., Salvarani, F.: 1D nonlinear Fokker–Planck equations for fermions and bosons. Appl. Math. Lett. 21, 148–154 (2008)

Chai, G., Wang, T.J.: Mixed generalized Hermite–Fourier spectral method for Fokker–Planck equation of periodic field. Appl. Numer. Math. 133, 25–40 (2018)

Chavanis, P.H., Laurencot, P., Lemou, M.: Chapman–Enskog derivation of the generalized Smoluchowski equation. Phys. A 341, 145–164 (2004)

Christov, C.I.: A complete orthonormal system of functions in $$L^2(-\infty,\infty )$$ L 2 ( - ∞ , ∞ ) space. SIAM J. Appl. Math. 42, 1337–1344 (1982)

Coulaud, O., Funaro, D., Kavian, O.: Laguerre spectral approximation of elliptic problems in exterior domains. Comput. Mech. Appl. Mech. Eng. 80, 451–458 (1990)

Escobedo, M., Mischler, S.: On a quantum Boltzmann equation for a gas of photons. J. Math. Pures Appl. 80, 471–515 (2001)

Johnson Fox, C.M., Guo, B.Y., Tang, T.: Combined Hermite spectral-finite difference method for the Fokker–Planck equation. Math. Comput. 71, 1497–1528 (2001)

Frank, T.D.: Nonlinear Fokker–Planck Equations: Fundamentals and Applications, Springer Series in Synergetics. Springer-Verlag, Berlin (2005)

Funaro, D.: Polynomial Approxiamtions of Differential Equations. Springer-Verlag, Berlin (1992)

Funaro, D., Kavian, O.: Approximation of some diffusion evolution equation in unbounded domains by Hermite function. Math. Comput. 57, 597–619 (1999)

Guo, B.Y.: Spectral Methods and Their Applications. World Scientific, Singapore (1998)

Guo, B.Y.: Error estimation of Hermite spectral method for nonlinear partial differential equations. Math. Comput. 68, 1069–1078 (1999)

Guo, B.Y.: Some developments in spectral methods for nonlinear partial differential equations in unbounded domains. In: Differential Geometry and Related Topics, pp. 68–90. World Scientific, Singapore (2002)

Guo, B.Y.: Some progress in spectral methods. Sci. China Math. 56, 2411–2438 (2013)

Guo, B.Y.: Spectral and pseudospectral methods for unbounded domains. Sci. China Math. 45, 975–1024 (2015)

Guo, B.Y., Ma, H.P.: Composite Legendre–Laguerre approximation in unbounded domains. J. Comput. Math. 19, 101–112 (2001)

Guo, B.Y., Shen, J.: Laguerre–Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math. 86, 635–654 (2000)

Guo, B.Y., Shen, J.: On spectral approximations using modified Legendre rational functions: application to Korteweg-de Vries equation on the half line. Indina Math. J. 50, 181–204 (2001)

Guo, B.Y., Shen, J., Wang, Z.Q.: A rational approximation and its applications to differential equations on the half line. J. Sci. Comput. 15, 117–147 (2000)

Guo, B.Y., Shen, J., Wang, Z.Q.: Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Int. J. Numer. Methods Eng. 53, 65–84 (2002)

Guo, B.Y., Shen, J., Xu, C.L.: Spectral and pseudospectral approximations using Hermite functions: application to the Dirac equation. Adv. Comput. Math. 19, 35–55 (2003)

Guo, B.Y., Shen, J., Xu, C.L.: Generalized Laguerre approximation and its applications to exterion problems. J. Comput. Math. 23, 113–130 (2005)

Guo, B.Y., Wang, L.L., Wang, Z.Q.: Generalized Laguerre interpolation and pseudospectral method for unbounded domains. SIAM J. Numer. Anal. 43, 2567–2589 (2006)

Guo, B.Y., Wang, T.J.: Composite generalized Laguerre–Legendre spectral method for exterior problems. Adv. Comput. Math. 32, 393–429 (2010)

Guo, B.Y., Wang, T.J.: Composite generalized Laguerre–Legendre spectral method with domain decomposition and its application to Fokker–Planck equation in an infinite channel. Math. Comput. 78, 129–151 (2009)

Guo, B.Y., Zhang, K.J.: Non-isotropic Jacobi pseudospectral method. J. Comput. Math 26, 511–535 (2008)

Guo, B.Y., Zhang, X.Y.: Spectral method for differential equations of degenerate type by using generalized Laguerre functions. Appl. Numer. Math. 57, 455–471 (2007)

Kaniadakis, G.: Generalized Boltzmann equation describing the dynamics of bosons and fermions. Phys. Lett. A 203, 229–234 (1995)

Lu, X.G.: On spatially homogeneous solutions of a modified Boltzmann equation for Fermi–Dirac particles. J. Stat. Phys. 105, 353–388 (2001)

Maday, Y., Pernaud-Thomas, B., Vandeven, H.: One réhabilitation des méthods spèctrales de type Laguerre. Rech. Aérospat. 6, 353–379 (1985)

Mastroianni, G., Occorsio, D.: Lagrange interpolation at Laguerre zeros in some weighted uniform spaces. Acta Math. Hung. 91, 27–52 (2001)

Shen, J.: A new fast Chebyshev–Fourier algorithm for the Poisson-type equations in polar geometries. Appl. Numer. Math. 33, 183–190 (2000)

Shen, J.: Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal. 38, 1113–1133 (2000)

Shen, J., Wang, L.L.: Some recent advances on spectral methods for unbounded domains. Commun. Comput. Phys. 5, 195–241 (2009)

Wang, T.J.: Laguerre pseudospectral method for nonlinear heat transfer equation on semi-infinite interval. Commun. Appl. Math. Comput. 27, 9–15 (2013)

Wang, T.J.: Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equation on the whole line. Math. Methods. Appl. Sci. 40, 1462–1474 (2017)

Wang, T.J., Guo, B.Y.: Composite generalized Laguerre–Legendre pseudospectral method for Fokker–Planck equation in an infinite channel. Appl. Numer. Math. 58, 1448–1466 (2008)

Wang, Z.Q., Guo, B.Y.: A rational approximation and its applications to nonlinear partial differential equations on the whole line. J. Math. Anal. Appl. 274, 374–403 (2002)

Wang, Z.Q., Guo, B.Y., Zhang, W.: Mixed spectral method for three-dimensional exterior problems using spherical harmonic and generalized Laguerre functions. J. Comput. Appl. Math. 217, 271–298 (2008)

Xu, C.L., Guo, B.Y.: Mixed Laguerre–Legendre spectral method for incompressible flow in an infinite strip. Adv. Comput. Math. 16, 77–96 (2002)

Xu, C.L., Guo, B.Y.: Laguerre pseudospectral method for nonlinear partial differential equations. J. Comput. Math. 20, 413–428 (2002)

Xu, C.L., Guo, B.Y.: Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions. Appl. Math. Mech. 29, 311–331 (2008)

Zhang, C., Guo, B.Y.: Domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations on unbounded domains. J. Sci. Comput. 53, 451–480 (2012)