In this paper, the Adomian decomposition method for the approximate solution of generalized Korteweg de Vries equation with boundary conditions is implemented. By using this method, the solution is calculated in the form of power series. The method does not need linearization, weak nonlinearity or perturbation theory. By using Mathematica Program, Adomian polynomials of the obtained series solu...

New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.

The Modified Regularized Long Wave (MRLW) equation is solved numerically by Adomian decomposition method (ADM) with some initial conditions. The method leads to high accurate and efficient results. Three polynomial invariant conditions are evaluated to determine the conservation properties of the problem. The convergence of Adomian decomposition method applied to the MRLW equation is proved. Mo...

Adomian decomposition method, as a convenience device has been used to solve many functional equations so far. In this manuscript, we consider a system of nonlinear ordinary differential equations, which governs on general reaction in biochemistry as a theoretical problem of concentration kinetics. These system, which is known as Brusselator system has been solved by applying Adomian decomposit...

We prove convergence of the Adomian decomposition method for an abstract initial-value problem using the method of majorants from the Cauchy-Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq...

The aim of this study is applying the Multistage Adomian Decomposition Method (MADM), based on the Adomian Decomposition Method (ADM) to solve an initial value problem of Bratu-type. The approximat-ed solutions are computed and then the numerical results compared those of ADM, Finally comparisons of the results show that the pro-posed method is very effective and accurate.

In this paper, the existence and uniqueness theorems for a solution to an uncertain characteristic Cauchy reaction-diffusion problem is studied by Adomian decomposition method. Sufficient conditions are presented for uniform convergence of the proposed method. Also, some illustrative examples are given for solving the problem. Key WordsUncertain characteristic Cauchy problem, System of characte...

Adomian polynomials are constituted of reduced polynomials and derivatives of nonlinear operator. The reduced polynomials are independent of the form of the nonlinear operator. A recursive algorithm of the reduced polynomials is discovered and its symbolic implementation by the software Mathematica is given. As a result, a new and convenient algorithm for the Adomian polynomials is obtained.

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability. Keywords—Fuzzy-valued function, Fuzzy initial value...

Abstract: Convergence of Adomian decomposition method (ADM) is ofa great importance when applied to different types of linear and nonlinear equations.In this paper, a general proof of convergence of ADM is introduced. In this work, a reliable approach for convergence of the Adomian method is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of t...