In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM; numerical results are discussed, compared with exact soluti...

The combined effects of nanoparticle and magnetic field on the nonlinear Jeffery-Hamel flow are analyzed in the present study. The basic governing equations are solved analytically to nonlinear ordinary differential equation using perturbation method together with a semi-numerical analytical technique called Hermite- Padé approximation. The obtained results are well agreed with that of the Adom...

Solving Nonlinear Klein-Gordon Equation with a Quadratic Nonlinear term using Homotopy Analysis Method H. Jafari , M. Saeidy, M. Arab Firoozjaee Department of Mathematics and Computer Science, University of Mazandaran, P. O. Box 47416-1467, Babolsar, Iran. Abstract In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy...

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...

The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obt...

This work proposes and investigates the existence uniqueness of solutions Riccati Fractional Differential Equation (RFDE) with constant coefficients using Banach’s fixed point theorem. theorem is a on contraction mapping norm space. Furthermore, combined Adomian Decomposition Method (ADM) Kamal’s Integral Transform (KIT) used to convert solution (FDE) into an infinite polynomial series. In addi...

An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) modified via introducing a functional term involving both variable parameter. A residual approach then adopted to identify optimal value embedded parameter within frame L2 norm. Numerical experiments on sample problems open lite...

In this work, a new technique based on Green’s function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solv...

In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition (SDM), then use to solve generalized Hirota-Satsuma Coupled kdv (H-SC kdv) systems also applied STM, find approximate solutions of system one. Then compare way exact solitary solutions. Clarifying best through tables d...

In [M.M. Hosseini, Adomian decomposition method with Chebyshev polynomials, Appl. Math. Comput., in press] an efficient modification of the Adomian decomposition method was presented by using Chebyshev polynomials. Also, in [M.M. Hosseini, Adomian decomposition method for solution of differential algebraic equations, J. Comput. Appl. Math., in press] solution of linear differential algebraic eq...