A Compact Finite Difference Method for the Solution of the Generalized Burgers-Fisher Equation

SARI M., GÜRARSLAN G., Dag İ.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.26, sa.1, ss.125-134, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 1
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1002/num.20421
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.125-134
  • Anahtar Kelimeler: compact finite difference method, generalized Burgers-Fisher equation, nonlinear PDE, Fisher equation, PARABOLIC EQUATIONS, SCHEMES, SIMULATION
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this article, numerical Solutions of the generalized Burgers-Fisher equation are obtained using compact finite difference method with minimal compuatational 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 Runge-Kutta 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. (C) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 125-134, 2010