THE ADOMIAN DECOMPOSITION METHOD AND MODIFIED DECOMPOSITION FOR SOLVING PARTIAL DIFFERENTIAL EQUATION

Abstract

In this research we study the solution of partial differential equations using Adomian decomposition method (ADM) and modified decomposition (MD) and we compared between the results of the two methods. In chapter one we explained the two methods and how to use them to solve initial value problem of ordinary differential equations (ODE) and gave some examples with comparison of the result founded by using ADM and MD . In chapter two we explain how to use ADM in solving partial differential equation and we takes some example of boundary value problems, we also compare the results founded with the exact solution. In chapter three we solve partial differential equations using MD .First we explain MD in several dimensions and we solve some example of boundary value problem we also compare the results with the solution founded by ADM and we use MD to solve Nonlinear partial differential equations. In chapter four concentrates on results obtained by using ADM for solving some types of partial differential equations like Non linear heat equation, Fokker-Plank equation and parabolic equation and we solve heat and wave equation using MD that is the results of MD are more accurate or the same aquantitative solutions and its simple to apply.