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 algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the ...

The aim of this paper is to present the application of the analytical series technique to study properties of the nonlinear chaotic dynamical systems. More specifically, Laplace–Adomian decomposition method is applied to Rössler system and the so-called generalized Lorenz system. Some advantages and possible applications of this approach are discussed. Results are illustrated by numerical compu...

We present a new discrete Adomian decomposition method to approximate the theoretical solution of discrete nonlinear Schrödinger equations. The method is examined for plane waves and for single soliton waves in case of continuous, semi– discrete and fully discrete Schrödinger equations. Several illustrative examples and Mathematica program codes are presented.

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.

This work presents a theoretical analysis for the Black–Scholes equation. Given a terminal condition, the analytical solution of the Black–Scholes equation is obtained by using the Adomian approximate decomposition technique. The mathematical technique employed in this work also has significance in studying some other problems in finance theory.

In this paper, we consider differential-algebraic equations(DAEs) systems . The approximate solutions for the differential-algebraic equations(DAEs) systems are obtained by using the Adomian decomposition method. The method is illustrated by two examples of differential-algebraic equations(DAEs) systems and series solutions are obtained. The solutions have been compared with those obtained by e...

In this paper a numerical algorithm, based on the Adomian decomposition method and a modified form of this method, is presented for solving a system of second-order boundary value problems associated with obstacle, unilateral, and contact problems. The scheme is shown to be highly accurate, and only a few terms are required to obtain accurate computable solutions.