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.

This paper deals with the numerical study of multi-scroll hyperchaotic attractors via the Adomian decomposition method. This objective is achieved by exploiting Hermite interpolating polynomials as nonlinearities in coupled Chua’s circuits. Several examples of generation of multi-scroll attractors highlight the capabilities of the proposed technique.

In this article Adomian decomposition method, as a well-known method for solving functional equations, has been employed to solve systems of Integral–differential equations. Theoretical considerations are discussed, and convergence of the method for these systems is addressed. Some examples are presented to show the ability of the method for such systems. 2004 Elsevier Inc. All rights reserved.

Recently, Wazwaz [Appl. Math. Comput. 118 (2001) 311–325] applied the Adomian s decomposition method to solve analytically the solution of sixth-order boundary value problems. The same problem is discussed via the variational principle, which reveals to be much more simpler and much more efficient. 2002 Elsevier Science Inc. All rights reserved.

In this paper, an analytical approximation to the solution of higher order Korteweg-de Vries (KdV) equations has been studied. The Homotopy Perturbation Method (HPM) introduced by He is employed to drive this analytical solution and the results will be compared with those of the Adomian decomposition method. Numerical results reveal that the HPM provides highly accurate numerical solutions for ...

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.