A comparison of Adomian and generalized Adomian methods in solving the nonlinear problem of flow in convergent-divergent channels

Abstract

The principal aim of this paper is to compare two analytical methods of decomposition employed for solving nonlinear problem of flow in converging-diverging channels, namely the Adomian Decomposition Method (ADM) and Generalized Decomposition Method (GDM). The comparison between ADM and GDM is conducted by using the numerical results of the studied problem as a guide. The results show that GDM method is more accurate and very efficient than ADM method. Indeed, ADM is a good method in solving the nonlinear problems, but we notice in solving the nonlinear problem of the Jeffery-Hamel flow that GDM is powerful, superior than ADM and clearly constitute an excellent choice for solving nonlinear problems.