Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 370765, 11 pages
doi:10.1155/2009/370765
Research Article

Numerical Solutions of the Generalized Burgers-Huxley Equation by a Differential Quadrature Method

Murat Sari1 and Gürhan Gürarslan2

1Department of Mathematics, Faculty of Art and Science, Pamukkale University, 20070 Denizli, Turkey
2Department of Civil Engineering, Faculty of Engineering, Pamukkale University, 20070 Denizli, Turkey

Received 29 July 2008; Accepted 26 January 2009

Academic Editor: Francesco Pellicano

Copyright © 2009 Murat Sari and Gürhan Gürarslan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation is obtained easily. The effectiveness of this method is verified through illustrative examples. The present method is seen to be a very reliable alternative method to some existing techniques for such realistic problems.