The approximate solutions for the Burger’s–Huxley and Burger’s–Fisher equations are obtained by using the Adomian decomposition method [Solving Frontier Problems of Physics: the Decomposition Method, Kluwer, Boston, 1994]. The algorithm is illustrated by studying an initial value problem. The obtained results are presented and only few terms of the expansion are required to obtain the approxima...

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 provides a comparative study of the Variational Iteration Method (VIM) and the Adomian Decomposition Method (ADM) to obtain analytic approximations of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. An excellent agreement is observed between the series solutions for the velocity field obtained by these two methods. This comparison is ben...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

Adomian s decomposition method (ADM) is proposed to approximate the numerical and analytical solutions of system two-dimensional Burgers equations (STDBE) with initial conditions. The advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence. Some examples are given to illustrate the performance of the m...

In the research, nonlinear volterra partial integro-differential equation is considered. This paper compares the Homotopy Perturbation Method (HPM) with Variational Iteration Method (VIM) for solving this equation. Compared with the Adomian Decomposition Method (ADM), the methods used for this equation need less work. The results of applying these methods show the simplicity and efficiency of t...

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.