Combined Hermite spectral-finite difference method for the Fokker-Planck equation

Johnson C.M. Fok*, Benyu Guo, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and is shown to improve the accuracy and effectiveness of the Hermite spectral approximation, with no increase in workload. Some basic analysis for the selection of the scaling factors is also presented.

Original languageEnglish
Pages (from-to)1497-1528
Number of pages32
JournalMathematics of Computation
Volume71
Issue number240
DOIs
Publication statusPublished - Oct 2002

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Error analysis
  • Finite-difference method
  • Fokker-Planck equation
  • Hermite spectral method
  • Unbounded domain

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