An extension of the decomposition method for solving nonlinear equations and its convergence

In this paper, we propose an extension of the decomposition method for solving nonlinear equations. After a summary of Adomian’s decomposition method (ADM), a new kind of decomposition strategy for nonlinear functions in nonlinear equations is proposed, and a generalized decomposition method (GDM) for solving nonlinear equations is presented. Under a rather mild condition, the convergence of the GDM is proved. Also, some concrete examples are studied to illustrate with numerical results how powerful the GDM is. Finally, some general remarks conclude this study.