Numerical study of Fisher's reaction-diffusion equation by the Sinc collocation method

Kamel Al-Khaled

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.

Original languageEnglish
Pages (from-to)245-255
Number of pages11
JournalJournal of Computational and Applied Mathematics
Volume137
Issue number2
DOIs
Publication statusPublished - Dec 15 2001

Keywords

  • Fisher's equation
  • Nonlinear parabolic equation
  • Reaction-diffusion equations

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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