SOLVING 1-DIMENSIONAL DIFFUSION PROCESS BY PADE APPROXIMATION

Abstract

This paper explores the method of Pade approximation to solve a system of heat equation; The Pade method of solving PDEs is a well-established method because of its added advantage of naturally increasing the domain of convergence of truncated power series. The solution of the heat equation has been directly expressed as a rational power series of the independent variable known as the Pade approximant. Attempt is made to solve the heat equation and obtain solutions in terms of their exponential matrix. A test on the stability of the solutions via conventional numerical procedures through some form of John Neumann stability method confirmed the scheme to be  and therefore produced solutions that are well behaved.