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