Applications of the decomposition method

We consider different applications of Adomian Decomposition Method. The Decomposition method will be applied fort he solution of Ordinary and Partial Differential Equations. We consider the Linear and Non-linear differential equations. The solution received will be infinite series solution and terms of the series easily can be calculated. First we classify the Decomposition Method and then explain some properties of so-called Adomian polynoials. At the end we solve some problems related with the application of Adomian Decomposition Method.Keywords: Adomian Decomposition Method,Adomian polynomials, Series solution