Year: 2001
Author: Geng Sun, Hua-Mo Wu, Li-Er Wang
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 519–530
Abstract
A new class of finite difference schemes is constructed for Fisher partial differential equation i.e. the reaction-diffusion equation with stiff source term: $au(1-u)$. These schemes have the properties that they reduce to high fidelity algorithms in the diffusion-free case namely in which the numerical solutions preserve the properties in the exact solutions for arbitrary time step-size and reaction coefficient α＞0 and all nonphysical spurious solutions including bifurcations and chaos that normally appear in the standard discrete models of Fisher partial differential equation will not occur. The implicit schemes so developed obtain the numerical solutions by solving a single linear algebraic system at each step. The boundness and asymptotic behaviour of numerical solutions obtained by all these schemes are given. The approach constructing the above schemes can be extended to reaction-diffusion equations with other stiff source terms.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-9004
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 519–530
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Reaction-diffusion equation Fidelity algorithm.