High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

Murat Sari*, Gürhan Gürarslan, Asuman Zeytinoälu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

Abstract

In this article, up to tenth-order finite difference schemes are proposed to solve the generalized Burgers-Huxley equation. The schemes based on high-order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high-order schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high-order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers-Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications.

Original languageEnglish
Pages (from-to)1313-1326
Number of pages14
JournalNumerical Methods for Partial Differential Equations
Volume27
Issue number5
DOIs
Publication statusPublished - Sept 2011
Externally publishedYes

Keywords

  • Burgers-Huxley equation
  • high-order finite difference schemes
  • nonlinear PDE
  • Runge-Kutta

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