Table of Contents
Chinese Journal of Mathematics
Volume 2014 (2014), Article ID 313691, 7 pages
http://dx.doi.org/10.1155/2014/313691
Research Article

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

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan

Received 14 September 2013; Accepted 15 December 2013; Published 29 January 2014

Academic Editors: T. Calvo, V. Oliker, and Z. Wang

Copyright © 2014 Fiza Zafar and Gulshan Bibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 , if 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 . Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.