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A Discrete KPP-Theory for Fisher's Equation

Bengt Hakberg (Institutionen för matematiska vetenskaper)
Mathematics of Computation (0025-5718). Vol. 82 (2013), 282, p. 781-802.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2013-11-29. Senast ändrad 2016-11-07.
CPL Pubid: 187842

 

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Matematik

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