Exact and Numerical Solutions to the Cauchy Problem

The aim of this paper is to consider the cauchy problem for a porous medium equation with a source term using the homotopy perturbation method (HPM). This equation has been widely used as a simple model for a nonlinear heat propagation in a reactive medium We obtain a series solution of porous media equation with a source term by using HPM. Application of this technique to this problem shows the rapid convergence of the sequence constructed by these methods to the exact solution. The results show applicability, accuracy and efficiency of HPM in solving nonlinear differential equations.