Use of He's Homotopy Perturbation Method for solving a partial differential equation arising in modeling of flow in porous media

The Boussinesq-type equations serve as models in many branches of science and engineering. Recently, much attention has been expended in studying these equations, and there has been a considerable mathematical interest in them. In this work, we present the solution of a generalized Boussinesq equation by means of the homotopy perturbation method. The homotopy perturbation method is an analytical procedure for finding the solutions of differential equations that is based on constructing a homotopy with an imbedding parameter p is an element of [0, 1], which is considered to be a so-called small parameter Application of the homotopy perturbation technique to this problem shows the rapid convergence of this method to the exact solution. The approximations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. Moreover, this technique does not require any discretization, linearization, or small perturbations and therefore reduces the numerical computations by a great deal.