Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation. (10th May 2010)

• Record Type: Journal Article
• Authors: Zakeri, Ali; Aminataei, Azim; Jannati, Qodsiyeh
• Other Names: Robnik Marko Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2010(2010)
• Publication Date: 2010-05-10
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2010/780207
• Languages: English
• ISSNs: 1026-0226

Abstract

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.