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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 878349, 13 pages
http://dx.doi.org/10.1155/2012/878349
Research Article

Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method

1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
2Department of Mathematics, Faculty of Science, University of Kordofan, North Kordofan State, Elobeid 51111, Sudan
3Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
4Department of Computer Science and Information System, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia

Received 11 June 2012; Accepted 25 July 2012

Academic Editor: Saeid Abbasbandy

Copyright © 2012 Mojtaba Nazari et al. 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

The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter , which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.