Some Third-Order Modifications of Newton’s Method

In this paper a new family of methods, free from second derivative, is presented. This new family of methods is constructed such that convergence is of order three and requires two require two evaluations of the function and first derivative per iteration. To illustrate the efficiency and performance of the new family of methods, several numerical examples are presented. Further numerical comparisons are made with several other existing third-order methods to show the abilities of the presented family of methods.