Some iterative methods free from second derivatives for nonlinear equations

In a recent paper, Noor [M. Aslam Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 2007, doi:10.1016/j.amc:2007], suggested and analyzed a generalized one parameter Halley method for solving nonlinear equations using. In this paper, we modified this method which has fourth order convergence. As special cases, we obtain a family of third-order iterative methods for appropriate and suitable choice of the parameter. We have compared this modified Noor method with some other iterative methods which shows that this new iterative method is robust and efficient one. Several examples are given to illustrate the efficiency and the performance of this new method.