Examples of modelling with Adomian decompositon method

This article is a report on, unlike any other numerical methods, using Adomian Decomposition Method (ADM) is pointed out to solve more easily and accurately without transforming the equation. Moreover, the ADM which is a powerful method to investigate approximate solutions or even analytical solutions of nonlinear equations, is explained with examples. This situation is also seem that is an undeniable advantage for samples resolved with ADM which have very rapidly convergent.In chapter one, it has given knowledge about G. Adomian and reviewed literature of method. Within hypothesis and purposes is started other sections.In chapter two, firstly, analysis of method is expressed an example. Afterwards, the theorems are given interested in convergence and Adomian Polynomials are calculated with samples of three different methods such as Taylor Series Method, Neumann Series Method and Parametrization. In addition, Modified Decomposition Method is analyzed and is compared with standard Adomian Decomposition Method. Finally, using Picard Method and AAM have been commented about the solutions of same examples.In the first part of section three, applications are available for ordinary differential equations. In the second part of the same section, the various examples for the partial differential equations are given interested in heat and wave equations. In the third part of the section three, the information is provided about systems of equations. In the fourth part of the section three, solving the integral equations with the Adomian Decomposition method and in the finally part, it is made the disclosure about of integro-differential equations.In conclusion, in this research, the utilizing from the opportunity of the method are obtained more efficiency and elegantly results in several types of equations with ADM.