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A discrete KPP-theory for Fisher's equation

Author: Bengt Hakberg
Journal: Math. Comp. 82 (2013), 781-802
MSC (2010): Primary 65M06
Published electronically: August 21, 2012
MathSciNet review: 3008838
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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.

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Additional Information

Bengt Hakberg
Affiliation: Department of Mathematical Sciences, Chalmers and Gothenburg University, S-41296 Goteborg, Sweden

Received by editor(s): December 6, 2010
Received by editor(s) in revised form: October 11, 2011
Published electronically: August 21, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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