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.

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 the generalized Fisher’s equation to o...

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...

By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

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. ...

a 2-d heat conduction model has been solved by using the adomian decomposition method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.the laser source may operate in a continuous wave (cw) mode or repeated pulse (rp) mode and may havearbitrary, spatial and temporal profiles.a generalized solution containing five-terms approxim...