One-Parameter Third-Order Iterative Methods for Solving Nonlinear Equations

In this paper, we present a modification of the two-step Newton´s method which produces a class of one-parameter iterative methods for solving nonlinear equations. An interpolating polynomial is constructed to avoid the evaluation of derivative. The convergence analysis shows that the new methods are third-order convergent and require one function and two first derivative evaluations per iteration. Several numerical examples are given to illustrate the performance of the presented methods.