A discrete KPP-theory for Fisher’s equation
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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.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