Adomian s decomposition method (ADM) is proposed to approximate the numerical and analytical solutions of system two-dimensional Burgers equations (STDBE) with initial conditions. The advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence. Some examples are given to illustrate the performance of the m...

In this work, the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM) are applied to solve the Rosenau–Hyman equation. We used the initial condition ( u(x, 0) = −83 cos 2 ( x 4 )) for aforementioned methods. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of h...

In this paper, we use an efficient numerical algorithm for solving two point fourth-order linear and nonlinear boundary value problems, which is based on the Adomian decomposition method (ADM), namely, the extended ADM (EADM). The proposed method is examined by comparing the results with other methods. Numerical results show that the proposed method is much more efficient and accurate than othe...

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, Sumudu decomposition method is developed to solve general form of fractional partial differential equation. The proposed method is based on the application of Sumudu transform to nonlinear fractional partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivatives are described in the Caputo sense. The Sumud...

Although there has been increased interest in the application of the stable and geometric stable distributions in economics and finance, further application has been limited because their probability density function does not have an explicit solution. In this paper, we present three analytic approximation methods — homotopy perturbation method, Adomian decomposition method, and variational ite...

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 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.