Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method

In this paper, we present some efficient numerical algorithms for solving nonlinear equations based on Newton–Raphson method by using modified homotopy perturbation method. The modified Adomian decomposition method [S. Abbasbandy, Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 145 (2003) 887–893], is compared with new algorithms. Some numerical illustrations are given to show the efficiency of algorithms.