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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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A discrete KPP-theory for Fisher’s equation
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by Bengt Hakberg PDF
Math. Comp. 82 (2013), 781-802 Request permission

Abstract:

The purpose of this paper is to extend the theory by Kolmogorov, Petrowsky and Piscunov (KPP) for Fisher’s equation, to a discrete solution. We approximate the time derivative in Fisher’s equation by an explicit Euler scheme and the diffusion operator by a symmetric difference scheme of second order. We prove that the discrete solution converges towards a traveling wave, under restrictions in the time- and space-widths, as the number of time steps increases to infinity. We also prove that the flame velocity can be determined as a solution to an optimization problem.
References
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Additional Information
  • Bengt Hakberg
  • Affiliation: Department of Mathematical Sciences, Chalmers and Gothenburg University, S-41296 Goteborg, Sweden
  • Email: hakberg@chalmers.se
  • Received by editor(s): December 6, 2010
  • Received by editor(s) in revised form: October 11, 2011
  • Published electronically: August 21, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 82 (2013), 781-802
  • MSC (2010): Primary 65M06
  • DOI: https://doi.org/10.1090/S0025-5718-2012-02642-1
  • MathSciNet review: 3008838