High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation

Sari M., Gurarslan G., ZEYTİNOĞLU A.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, vol.27, no.8, pp.1296-1308, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 8
  • Publication Date: 2011
  • Doi Number: 10.1002/cnm.1360
  • Journal Name: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1296-1308
  • Keywords: generalized Burgers-Fisher equation, nonlinear PDE, high-order finite difference scheme, Fisher equation
  • Istanbul Technical University Affiliated: No

Abstract

Up to tenth-order finite difference (FD) schemes are proposed in this paper to solve the generalized Burgers-Fisher equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order FD schemes in space and fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the present methods. The produced results are also seen to be more accurate than some available results given in the literature. Comparisons showed that there is very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present methods are seen to be very good alternatives to some existing techniques for such realistic problems. Copyright (C) 2009 John Wiley & Sons, Ltd.