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, 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.

Adomian decomposition method (ADM) is applied to approximately solve stochastic fractional integrodifferential equations involving nonlocal initial condition. The convergence of the ADM for the considered problem is proved. The mean square error between approximate solution and accurate solution is also given. [Mahmoud M. El-Borai, M.A.Abdou, Mohamed Ibrahim M. Youssef. On Adomian’s Decompositi...

This paper compares the variational iteration method (VIM) with the Adomian decomposition method (ADM) for solving nonlinear integrodifferential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use.

This paper provides a comparative study of the Variational Iteration Method (VIM) and the Adomian Decomposition Method (ADM) to obtain analytic approximations of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. An excellent agreement is observed between the series solutions for the velocity field obtained by these two methods. This comparison is ben...

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three...

The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear p...

In this paper, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

Abstract: In this article, we develop a method to obtain approximate solutions of nonlinear coupled partial differential equations with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this...

We prove convergence of the Adomian Decomposition Method (ADM) by using the Cauchy-Kovalevskaya theorem for differential equations with analytic vector fields, and obtain a new result on the convergence rate of the ADM. Picard's iterative method is considered for the same class of equations in comparison with the decomposition method. We outline some substantial differences between the two meth...