Study of the Modified Decomposition Method for Solving Partial Differential Equations with Application to Luikov’s System

Abstract

In this dissertation we study the solution of system of partial differential equations (SPDE) 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 partial differential equations (PDE) and gave some examples with comparison of the result founded by using ADM and MD.

In chapter two we explain how to use ADM and MD in solving boundary value problem , and we gave two examples of boundary problems , Neumann problem for the vibrating string and Dirichlet boundary conditions.

Chapter three concentrates on applications of ADM and MD on Physical Models problems.

In chapter four we solve some linear and nonlinear systems of partial differential equations using ADM and compare the result found to that of MD.