Homotopy Perturbation Method (HPM) and the modified (HPM) for linear and nonlinear operators

Abstract

In this thesis we present the homotopy perturbation method (HPM). We applied it for solving some differential and integral equations (linear and nonlinear). The HPM is a coupling of the traditional perturbation method and homotopy in topology. This method doesn’t require a small parameter in an equations. It method provides an analytical approximate solution for the differential equations. We also present a modification of The homotopy perturbation method. and apply it also for solving linear and nonlinear differential equations. The modified HPM accelerates the rapid convergence of the series solution. The modification provides the exact solution by using only minimal number of iteration and improve the performance of the standard HPM .