Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 780207, 10 pages
doi:10.1155/2010/780207
Research Article

Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation

Ali Zakeri, Azim Aminataei, and Qodsiyeh Jannati

Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 1541849611 Tehran, Iran

Received 18 July 2009; Revised 14 March 2010; Accepted 31 March 2010

Academic Editor: Marko Robnik

Copyright © 2010 Ali Zakeri 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

We consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has a specified condition, the above solution can be estimated. Finally, a numerical experiment is provided to illustrate the method.