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

Authors: Johnson C. M. Fok, Benyu Guo and Tao Tang
Journal: Math. Comp. 71 (2002), 1497-1528
MSC (2000): Primary 65M12, 65M70; Secondary 82C31
Published electronically: December 21, 2001
MathSciNet review: 1933042
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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.

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Additional Information

Johnson C. M. Fok
Affiliation: Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Hong Kong

Benyu Guo
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

Tao Tang
Affiliation: Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Keywords: Fokker-Planck equation, unbounded domain, Hermite spectral method, finite-difference method, error analysis
Received by editor(s): December 13, 1999
Received by editor(s) in revised form: October 30, 2000
Published electronically: December 21, 2001
Additional Notes: This research was partially supported by FRG Grants of Hong Kong Baptist University and RGC Grants of Hong Kong Research Grants Council.
Article copyright: © Copyright 2001 American Mathematical Society