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

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  • Tan, Jia
  • Wang, Tian-jun

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.

Suggested Citation

  • Tan, Jia & Wang, Tian-jun, 2024. "A multi-domain spectral collocation method for the Fokker–Planck equation in an infinite channel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 533-551.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:533-551
    DOI: 10.1016/j.matcom.2024.02.014
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