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International Journal of Analysis
Volume 2014, Article ID 685796, 5 pages
http://dx.doi.org/10.1155/2014/685796
Research Article

A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations

Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan 987-98155, Iran

Received 11 November 2013; Revised 6 January 2014; Accepted 9 January 2014; Published 12 February 2014

Academic Editor: Ahmed Zayed

Copyright © 2014 Tahereh Eftekhari. 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

Based on iterative method proposed by Basto et al. (2006), we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root α of the nonlinear equation . This method has the efficiency index which equals . The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods.