NEW DEVELOPMENT OF ADOMIAN DECOMPOSITION METHOD FOR SOLVING SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This study attempts at Adomian Decomposition Method (ADM) for solving second order ordinary differential equations such as Multi singular equation, Bessel’s equation, and Oscillatory systems. The (ADM) results in many known equations, some of them are studied and investigated by mathematicians and researchers, while others are still not well researched yet. We give a new differential operator and invers differential operator to solve different types for initial value problem in the second order ordinary differential equation. There are some different situations that we will study and give the non-linear examples that lead us to the approximate solutions of exact solution.