The solutions of linear and nonlinear differential equations and analysis of numerical solutions

This study is constructed in six chapters.In chapter one, some fundamental definitions are given.In chapter two, it is made analyze of Adomian decomposition method, Homotopy analysis method and Homotopy perturbation method to obtain solutions of nonlinear partial differential equations.In chapter three, the derivation of Adomian decomposition method using the homotopy analysis method is made analysis.In chapter four, the ninth-order Korteweg-de Vries equation is made analyze as numerical, it is obtained series solutions which are Adomian decomposition method, Homotopy analysis method and Homotopy perturbation method apply to the ninth-order Korteweg-de Vries equation.In chapter five, it is compared analytic solution which are obtained series solution by in fourth chapter. The figure is obtained approximate solution function and analytic solution function.In chapter six, it is made a generalized assessment by Adomian decomposition method, Homotopy analysis method and Homotopy perturbation method.