THEORETICAL AND APPLIED STUDY ON ADOMIAN DECOMPOSITION METHOD AND MODIFIED DECOMPOSITION

Abstract

In this dissertation we study the solution of system of ordinary differential equations (SODE) 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 and showed how to use ADM to solve ODE with singular point. In chapter two we explain how to use ADM in solving SODE both linear and nonlinear, we also compare the results of the two methods used (separation method – direct application to ADM) for solving coupled system of Schrödinger equations. Chapter three concentrates on results obtained by using ADM and MD for solving the prey and predator problem. In chapter four we solve Lotka-Volterra model using MD and compare the result found to that of ADM and draw a general pattern for solving Lotka-Volterra model using ADM and MD.