Variational iteration method for unsteady flow of gas through a porous medium using Heʹs polynomials and Pade approximants

In this paper, we apply the variational iteration method using Heʹs polynomials for finding the analytical solution of unsteady flow of gas through a porous medium. The proposed method is an elegant combination of Heʹs variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The diagonal Pade approximants are effectively used in the analysis to capture the essential behavior of the solution and to determine the initial slope. A clear advantage of this technique over the decomposition method is that no calculation of Adomianʹs polynomials is needed.