• OPTIMAL METHODS OF EIGHTH-ORDER FOR SOLVING NONLINEAR EQUATIONS

Abstract

In this article, methods of optimal eighth-order iterative methods are presented. The new methods are developed by combining special case of Al-Subaihi's method of fourth-order and adding Newton’s method as a third step. Using the forward divided difference and three real-valued functions in the third step to increase the convergence order and reduce the number of function evaluations to be optimal. Numerical examples are provided to show the good performance of the new method.