Composite generalized Laguerre--Legendre pseudospectral method for Fokker--Planck equation in an infinite channel

Authors:
Tian-jun Wang;Ben-yu Guo
Affiliations:
Department of Mathematics and Physics, Henan University of Science and Technology, LuoYang, 471003, China;Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China and Division of Computational Science of E-Institute of Shanghai Universities, China
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 9
Cited 2

Laguerre spectral approximation of elliptic problems in exterior domains

ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Adaptive local overlapping grid methods for parabolic systems in two space dimensions

Journal of Computational Physics
Error estimation of Hermite spectral method for nonlinear partial differential equations

Mathematics of Computation
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions

SIAM Journal on Numerical Analysis
Combined Hermite spectral-finite difference method for the Fokker-Planck equation

Mathematics of Computation
Mixed laguerre-legendre pseudospectral method for incompressible fluid flow in an infinite strip

Mathematics of Computation
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

Journal of Approximation Theory
A new generalized Laguerre spectral approximation and its applications

Journal of Computational and Applied Mathematics
Generalized Laguerre Interpolation and Pseudospectral Method for Unbounded Domains

SIAM Journal on Numerical Analysis

Error analysis of Legendre spectral method with essential imposition of Neumann boundary condition

Applied Numerical Mathematics
Jacobi spectral method with essential imposition of Neumann boundary condition

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we propose a composite generalized Laguerre-Legendre pseudospectral method for the Fokker-Planck equation in an infinite channel, which behaves like a parabolic equation in one direction, and behaves like a hyperbolic equation in other direction. We establish some approximation results on the composite generalized Laguerre-Legendre-Gauss-Radau interpolation, with which the convergence of proposed composite scheme follows. An efficient implementation is provided. Numerical results show the spectral accuracy in space of this approach and coincide well with theoretical analysis. The approximation results and techniques developed in this paper are also very appropriate for many other problems on multiple-dimensional unbounded domains, which are not of standard types.