Iterative methods with fourth-order convergence for nonlinear equations

In this paper, we suggest and analyze a new three-step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to Noor [M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2006; M. Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput., in press] and Noor and Noor [M. Aslam Noor, K. Inayat Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., in press]. We show that this new iterative method has fourth-order convergence. Several numerical examples are given to illustrate the efficiency and performance of the new method.