Homotopy Perturbation Method for Systems of Partial Differential Equations

The homotopy perturbation method introduced by He [1-5] in 1998. Recently a great deal of interest has been focused on the applications of the homotopy perturbation method, well addressed in [6-14], In this method the solution is considered as the summation of an infinite series which usually converges rapidly to the exact solutions. This method has been used to solve wide variety mathematical problems. This method continuously deforms a simple problem, easy to solve, into the difficult problems under study. In this paper, we propose homotopy perturbation to solve systems of partial differential equations. These systems have attracted much attention in a variety of applied sciences. To illustrate the basic concept of homotopy perturbation method, consider the following nonlinear differential equation

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