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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Combined Hermite spectral-finite difference method for the Fokker-Planck equation
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by Johnson C. M. Fok, Benyu Guo and Tao Tang PDF
Math. Comp. 71 (2002), 1497-1528 Request permission

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
  • Email: cmfok@math.hkbu.edu.hk
  • Benyu Guo
  • Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China
  • Email: byguo@guomai.sh.cn
  • Tao Tang
  • Affiliation: Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Hong Kong.
  • Email: ttang@math.hkbu.edu.hk
  • 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.
  • © Copyright 2001 American Mathematical Society
  • Journal: Math. Comp. 71 (2002), 1497-1528
  • MSC (2000): Primary 65M12, 65M70; Secondary 82C31
  • DOI: https://doi.org/10.1090/S0025-5718-01-01365-5
  • MathSciNet review: 1933042