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.

We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the pr...

In the present work, entropy generation in the flow and heat transfer of couple stress fluid through an infinite inclined channel embedded in a saturated porous medium is presented. Due to the channel geometry, the asymmetrical slip conditions are imposed on the channel walls. The upper wall of the channel is subjected to a constant heat flux while the lower wall is insulated. The equations gov...

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...

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.

and reducing the problem to one of iteratively solving a linear equation for un once the previous iterates have been determined. However, Adomian partitions (1.4) into a sequence of linear ODEs in either x or t whose solutions cannot generally be made to satisfy the boundary and initial conditions. Even when applied to an initial value problem with boundary conditions, the convergence of the so...

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.

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.

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

In order to solve the local fractional differential equations, we couple residual method with Adomian decomposition via calculus operator. Several examples are given illustrate solution process and reliability of method.