We present a reliable algorithm for solving one-dimensional system of nonlinear partial differential equations. We investigate the numerical solution of this problem by using Adomian decomposition method (ADM). The solution is calculated in the form of a series with easily computable components. We prove the convergence of the ADM applied to nonlinear heat equation. Numerical experiments are pr...

In this paper, a numerical solution based on Adomian Decomposition Method (ADM) is used for finding the solution of higher order nonlinear problem which arise from the problems of calculus of variations. This approximation reduces the problem to an explicit system of algebraic equations. One numerical example is also given to illustrate the accuracy and applicability of the presented method.

Abstract : In this paper an interesting and famous realistic electronic circuit problem is discussed using the Adomian Decomposition Method (ADM) is presented. To illustrate the effectiveness of the ADM an example from linear time-varying electrical circuit problem have been considered and compared with the Runge-Kutta Butcher algorithm (RKB)[5] and with exact solutions of the problems, and are...

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.

In this paper, we show that with a few modifcations and techniques the Adomian Decomposition Method (ADM) for solving a class of hyperbolic equations with nonlocal conditions can be applied to obtain the exact solutions to this type of problems. The clue of this one consists in transforming the boundary value nonlocal problem into a classical problem whose solution is obtained.

in this paper, we apply the  homotopy analysis method (ham) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the ham. also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the ham is applied to linear system of equations. comparisons are made between the ...

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...

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.

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 letter, He’s Variational iteration method (VIM) is implemented for solving the nonlinear Whitham-Broer-Kaup partial differential equations. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by t...