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 ?₀−?????? and therefore produced solutions that are well behaved.