A compact finite difference method for the solution of the generalized burgers-fisher equation

Murat Sari*, Gürhan Gürarslan, Idris Daǧ

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

In this article, numerical solutions of the generalized Burgers-Fisher equation are obtained using a compact finite difference method with minimal computational effort. To verify this, a combination of a sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing RungeKutta scheme in time have been used. The computed results with the use of this technique have been compared with the exact solution to show the accuracy of it. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present method is seen to be a very good alternative to some existing techniques for realistic problems.

Original languageEnglish
Pages (from-to)125-134
Number of pages10
JournalNumerical Methods for Partial Differential Equations
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 2010
Externally publishedYes

Keywords

  • Compact finite difference method
  • Fisher equation
  • Generalized Burgers-Fisher equation
  • Nonlinear PDE

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