A multi-domain spectral collocation method for the Fokker–Planck equation in an infinite channel

Abstract

In this paper, we propose a multi-domain spectral collocation method for partial differential equations on two-dimensional unbounded domains. Some approximation results on the composite generalized Laguerre-Legendre interpolation and quasi-orthogonal projecting are established, respectively. These results play a significant role in related spectral collocation method. As an application, a multi-domain spectral collocation scheme is provided for the Fokker–Planck equation with absorption or non-homogeneous boundary conditions. The convergence of the proposed algorithm is performed. An efficient implementation is presented. Numerical experiments demonstrate the effectiveness and high accuracy of the algorithm.