Numerical solution of some nonlinear diferantial equations solutions by using homotopy perturbation method and adomian decomposition method

This study is constructed five chapters.In chapter one, some fundamental definitions are given.In chapter two, the primary structures of Homotopy Perturbation Method and Adomian Decomposition Method are given. And also the calculation Adomian polinoms which arise applying Adomian Decomposition Method are given.In chapter three, Homotopy Perturbation Method and Adomian Decomposition Method is applied to find approximate solutions of linear or nonlinear differential equations which have initial conditions such as KdV, Helmholtz, Dispersive, Klein-Gordon and nonlineer K(2,2) equations. We drawn graphics (2D and 3D) and constructed tables of approximate solutions and exact solution which are obtained for every equations.In chapter four, it is made a conversation of obtained datebases.In chapter five, it is suggested to apply Adomian Decomposition Method and Homotopy Perturbation Method to some linear or nonlinear differential equations by depending on obtained solutionsKey words: Adomian Decomposition Method, Homotopy Perturbation Method,KdV Equation, Helmholtz Equation, Dispersive Equation, Klein-GordonEquation, Nonlineer K(2,2) Equation.