A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

Abstract

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n + 10 , if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 14 1 / 5   = 1 . 695218203 . Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.