Iterative methods improving newtonʹs method by the decomposition method

In this paper, we present a sequence of iterative methods improving Newtonʹs method for solving nonlinear equations. The Adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses. The orders of convergence are derived analytically, and then rederived by applying symbolic computation of MAPLE. Some numerical illustrations are given.