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AN IMPROVED SECOND-ORDER NUMERICAL METHOD FOR THE GENERALIZED BURGERS–FISHER EQUATION

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Computer aspects of numerical algorithms Parabolic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  12 June 2013

A. G. BRATSOS
A. G. BRATSOS*
Affiliation:
Department of Mathematics, Technological Educational Institution (TEI) of Athens, 122 10 Egaleo, Athens, Greece
*
[email protected]
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Abstract

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A second-order in time finite-difference scheme using a modified predictor–corrector method is proposed for the numerical solution of the generalized Burgers–Fisher equation. The method introduced, which, in contrast to the classical predictor–corrector method is direct and uses updated values for the evaluation of the components of the unknown vector, is also analysed for stability. Its efficiency is tested for a single-kink wave by comparing experimental results with others selected from the available literature. Moreover, comparisons with the classical method and relevant analogous modified methods are given. Finally, the behaviour and physical meaning of the two-kink wave arising from the collision of two single-kink waves are examined.

Keywords

generalized Burgers–Fisher equationreaction–diffusion equationfinite-difference methodbistable mediumtravelling kink wavesmodified predictor–corrector method

MSC classification

Secondary: 35K57: Reaction-diffusion equations 35Q51: Soliton-like equations 65M06: Finite difference methods 65Y10: Algorithms for specific classes of architectures
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 3 , January 2013 , pp. 181 - 199
Copyright
Copyright ©2013 Australian Mathematical Society 

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