Exact solutions for some systems of PDEs by He's homotopy perturbation method

Abstract

In this paper, the homotopy perturbation method (HPM) proposed by Ji-Huan He is used to obtain approximate analytical solutions of systems of linear and nonlinear partial differential equations. The analytical solution of these systems is calculated in the form of a convergent power series with easily computable components. An efficient way of choosing the initial approximation is presented. To illustrate the ability and reliability of the method some examples are provided. The results prove that HPM is very effective and simple. Copyright © 2009 John Wiley & Sons, Ltd.