Modified Adomian decomposition method has been used intensively to solve linear and nonlinear singular boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. The method is illustrated by some examples of higher order ordinary equations systems and series ...

A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method ...

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...

In this paper, we use Sumudu Decomposition Method (SDM) ,which is combination of the Sumudu transform method and Adomian Decomposition Method, to obtain the approximate solutions of nonlinear systems of ordinary differential equations, particularly predator-prey systems. We can easily decompose the nonlinear terms by the help of Adomian polynomials. This technique provides a sequence of functio...

In this paper a recurrence technique for calculating Adomian polynomials is proposed, the convergence of the series for the Adomian polynomials is discussed, and the dependence of the convergent domain of the solution's decomposition series P 1 n¼0 u n on the initial component function u 0 is illustrated. By introducing the index vectors of the Adomian polynomi-als the recurrence relations of t...

The Telescoping Decomposition Method (TDM) is a new iterative method to obtain numerical and analytical solutions for first order nonlinear differential equations. The method is a modified form of the well-known Adomian Decomposition Method (ADM) where the Adomian polynomials have not to be calculating. The (TDM) is easier to apply and offers better accuracy than the (ADM). Also, it can be appl...

Solutions of differential algebraic equations is considered by Adomian decomposition method. In E. Babolian, M.M. Hosseini [Reducing index and spectral methods for differential-algebraic equations, J. Appl. Math. Comput. 140 (2003) 77] and M.M. Hosseini [An index reduction method for linear Hessenberg systems, J. Appl. Math. Comput., in press], an efficient technique to reduce index of semi-exp...

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...

In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. ...

Engineering problems and the solutions of many important physical problems are centered on finding accurate solutions to Nonlinear functions. Various approximation methods have been used for complex equations. One of the newest approximation methods is Reconstruction of variational iteration method (RVIM). In this Paper we use RVIM to solution N-soliton solutions for the fifth order Caudrey-Dod...