This paper investigates an initial-boundary value problem with nonlocal condition for the wave equation. The numerical solution is developed by using Homotopy perturbation method. This method is based on the use of traditional perturbation method and homotopy technique. Using this method, a rapid convergent series solution can be obtained in most cases. Furthermore, this method does not require...

More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput. 154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for the generalized Fisher’s equation to o...

Aim of the paper is to investigate applications of Homotopy Perturbation Method(HPM) on non-linear physical problems .Some coupled non-linear partial differential equations are considered and solved numerically using Homotopy Perturbation Method. The results obtained by HPM are compared with those obtained by Adomian Decomposition Method. The behavior of Homotopic solution is shown through grap...

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...

In this study, the implantation of a new semi-analytical method called optimal auxiliary function (OAFM) has been extended to partial differential equations. The adopted was tested upon for approximate solution generalized modified b-equation. first-order numerical obtained by OAFM compared with variational homotopy perturbation (VHPM). possesses and control parameters which can be easily handl...