Solution of initial value problems for nonlinear ordinary differential equations by adomian decomposition method

In this study, the approximate solutions of Initial Value Problems have been found for Nonlinear Ordinary Differential Equations by Adomian Decomposition Method.The various methods have been developed for the numerical solutions of ordinary differential equations. By help of rapidly developing computer technology, numerical solution methods developed are accompanied with analytic solution methods of linear and nonlinear differential equations. Adomian Decomposition Method was carried out by G.Adomian in 1980s. When we mention about Adomian Decomposition Method, we will use ADM for short. The Adomian Decomposition Method is one of the simple method according to other classical methods for solutions of nonlinear equations.ADM has been applied to the Engineering problems and gives more confident solutions. Maple-10 programme has been developed for deriving Adomian Polynoms? statements of some known nonlinear functions. Maple-10 programme has been used on calculations.In Chapter 1, The Existence and Unity Theorem and its Proof for Initial Value Problem with Basic Description and Theorems are given. In chapter 2, basic information about ADM are given. Chapter 2 consists of six parts. In Part 1,it has been mentioned about how to derive Adomian Polynomials.In Part 2, the application of ADM for Nonlinear Differential Equations System has been given. In Part 3, ADM has been applied to Nonlinear Ordinary Differential Equations. In Part 4, the application of ADM for Ordinary Differential Equations System are given. In Part 5, the application of ADM to the Heat Distribution Problem and Part 6; the application of ADM to Wave Equations have been given.Thus, ADM has obtained to find enough sensitive results to the real solution.Keywords: Adomian Decomposition Method, Heat equations, Nonlinear, Wave equations.