in this paper, we present a comparative study between the adomian decomposition method and two classical well-known runge-kutta and central difference methods for the solution of damped forced oscillator problem. we show that the adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.

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 ...

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.

Abstract:More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput. 154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for these equations to overcome t...

In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integrodifferential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the conve...

A generalized Fisher’s equation is solved by using the modified Adomian decomposition method MADM , variational iteration method VIM , homotopy analysis method HAM , and modified homotopy perturbation method MHPM . The approximation solution of this equation is calculated in the form of series whose components are computed easily. The existence, uniqueness, and convergence of the proposed metho...

In this work, conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity are evaluated using Adomian decomposition method. The results are compared with numerical and exact solutions. It is shown that the numerical simulation has some limitations and ma...

In recent publications [Chaos, Solitons Fractals 12 (2001) 2283; Int. J. Appl. Math. 3 (4) (2000) 361], we have dealt with the numerical solutions of the Korteweg–De-Vries (KDV) and modified Korteweg–De-Vries (MKDV) equations. We extend this study to a more general nonlinear equation, which is the general Korteweg–De-Vries (GKDV) equation, in which the previous studies is a special case of it. ...

This paper presents a technique for obtaining an exact solution the well-known Laguerre’s differential equations that arise in modeling of several phenomena quantum mechanics and engineering. We utilize efficient procedure based on modified Adomian decomposition method to obtain closed-form solutions associated equations. The proposed makes sense as attitudes acquired towards neighboring singul...