Solving Nonlinear Diffusion Equation of Porous Medium with linear pressure profile by Homotopy Perturbation Transform Method and He’s polynomials.

Abstract

Most physical phenomenon and processes in the field of Fluid Mechanics are governed by partial differential equations. Many nonlinear partial differential equations do not possess analytical solution, so numerical methods are commonly used to solve these equations. In this paper we have discussed an analytical method, which is a combination of Laplace Transforms and Homotopy Perturbation method called as homotopy perturbation transform method (HPTM). Our aim is to reduce the volume of computational work in finding the exact solution of nonlinear partial differential equation as compared to the classical methods while still maintaining the high accuracy of the numerical solution. One such nonlinear diffusion equation of porous medium with linear pressure profile is considered here with different initial conditions. Laplace Transform alone is incapable of handling nonlinear terms, so He’s polynomials are used to simplify the nonlinear terms appearing in the equation. Many researchers have used Adomian Polynomials to decompose the nonlinear terms of the partial differential equations arising in Fluid Mechanics. But the complexity and calculation process are much easier in HPTM compared to Adomian polynomials.