In this article we review the Adomian decomposition method (ADM) and its modifications including different modified and parametrized recursion schemes, the multistage ADM for initial value problems as well as the multistage ADM for boundary value problems, new developments of the method and its applications to linear or nonlinear and ordinary or partial differential equations, including fractio...

In this work, the solution of a boundary value problem is discussed via asemi analytical method. The purpose of the present paper is to inspect theapplication of the Adomian decomposition method for solving the Nagumotelegraph equation. The numerical solution is obtained for some special casesso that demonstrate the validity of method.

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

in this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. the convergence of the proposed method is given. to illustrate the proposed method, it is applied to a model for hiv infection of cd4+ t cells and the numerical results are compared with those of a recently proposed method.