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

Jia Tan and Tian-jun Wang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 533-551

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.

Keywords: The Fokker–Planck equation; Initial–boundary value problems; Unbounded domains; Multi-domain spectral collocation method; Composite interpolation approximation; Quasi-orthogonal projecting (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:533-551

DOI: 10.1016/j.matcom.2024.02.014

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