A new iterative method for solving nonlinear equations

摘要

In this paper, we present a new efficient iterative method for solving nonlinear equations improving Newton–Raphson method. This method is based on a modification of the proposal of Abbasbandy on improving the order of accuracy of Newton–Raphson method [S. Abbasbandy, Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 145 (2003) 887–893]. The convergence properties of the method and some other methods are discussed. Some numerical illustrations are given to show that the proposed method behaves equal or better performance compared to the other methods of same kind.