Coupled systems of two linear and nonlinear differential equations for secondand first-orders, respectively, can be solved with some techniques and Adomian decomposition method. A few simple examples are also studied to show with analytical results how the (ADM) works efficiently. 2005 Elsevier Inc. All rights reserved.

In this paper, the Adomian decomposition method for solving the linear and nonlinear parabolic equations is implemented with appropriate initial conditions. In comparison with existing techniques, the decomposition method is highly effective in terms of accuracy and rapid convergence. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of...

Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and a...

In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods. General Terms Numerical solutions, Fractional integro-differential equations.

To obtain the solution of nonlinear sequential fractional differential equations for Caputo operator two methods namely the Adomian decomposition method and DaftardarGejji and Jafari iterative method are applied in this paper. Finally some examples are presented to illustrate the efficiency of these methods. 2010 Mathematics Subject Classification: 65L05, 26A33

A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method ...

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.

In this paper, an application of Homotopy Analysis Method (HAM) is applied to solve the equation governing the unsteady flow of a polytropic gas. Comparison are made between the Adomian decomposition method and homotopy analysis method. The results reveal that the homotopy analysis method is very effective and simp le and gives the exact solution. Classification 2000 MSC: 34K28 • 35G25 • 34K17