We study approximate solutions of a nonlinear integral equation of Hammerstein type. We describe the principle of discrete Adomian decomposition method (DADM). DADM is considered in the case we evaluate numerical integration by using Chebyshev roots. This technique gives an accurate solutions as will shown by illustrate examples.

By studying Adomian decomposition method as well as its adaptabilities and capabilities, and by providing experiments, this article attempts to examine the barriers that arise in the course of calculating the above algorithm and that deflect us from the true solution.

Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: D i yi (x)=Ni(x, y1, . . . , yn), y i (0)= c k, 0 k [ i ], 1 i n and D i denotes Caputo fractional derivative. Some examples are solved as illustrations, using symbolic computation. © 2005 Elsevier B.V. All rights reserved.

This paper presents a new symbolic algorithm to compute the singular initial value problem of second-order ordinary differential equations using Adomian decomposition method. The algorithm has been implemented in the computer algebra system Maple to facilitate the application of this method. A number of examples are presented to demonstrate the computation efficiency of the program. 2005 Elsevi...

In this paper, an efficient modification of Adomian decomposition method is introduced for solving second order ordinary differential equations. The proposed method can be applied to singular and nonsingular problems. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method. 2006 Elsevier Inc. All rights reserved.

This work is an analytical study of unsteady thin film third grade fluid. The governing non linear partial differential equation has been solved analytically by Adomian Decomposition Method (ADM). The effect of model parameters on velocity profile have been plotted and discussed numerically as well as graphically.

In this paper an efficient modification of the Adomian decomposition method is presented by using Chebyshev polynomials. The proposed method can be applied to linear and non-linear models. The scheme is tested for some examples and the obtained results demonstrate reliability and efficiency of the proposed method. 2005 Elsevier Inc. All rights reserved.

In this paper, we consider Adomian Decomposition Method (ADM),and Variational Iteration Method (VIM), Homotopy Analysis Method (HAM), Homotopy Analysis Transform Method (HATM) to solve the FractionalOrder Logistic Equation (FOLE). Comparisons between the approximate analytical solution and exact solution of FOLE are shown. 2010 Mathematics Subject Classication: 34-XX , 34Lxx ,34L30

Nonlinear partial diferential equations are a class of partial diferential equations having many important uses in engineering and sciences. In this work we display a comparison between Adomian Decomposition Method (ADM) and Differential Quadrature Method (DQM) for solving some nonlinear partial diferential equations. We found the existence of exact solutions for those models. The numerical res...