Abstract and Applied Analysis
Volume 2013 (2013), Article ID 487062, 4 pages
http://dx.doi.org/10.1155/2013/487062
Research Article

A New Second-Order Iteration Method for Solving Nonlinear Equations

Shin Min Kang,1 Arif Rafiq,2 and Young Chel Kwun3

1Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
2School of Computer Science and Mathematics, Hajvery University, 43-52 Industrial Area, Gulberg III, Lahore 54660, Pakistan
3Department of Mathematics, Dong-A University, Busan 614-714, Republic of Korea

Received 26 January 2013; Accepted 13 March 2013

Academic Editor: Gue Lee

Copyright © 2013 Shin Min Kang et al. 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 establish a new second-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.4142 which is the same as the Newton-Raphson method. By using some examples, the efficiency of the method is also discussed. It is worth to note that (i) our method is performing very well in comparison to the fixed point method and the method discussed in Babolian and Biazar (2002) and (ii) our method is so simple to apply in comparison to the method discussed in Babolian and Biazar (2002) and involves only first-order derivative but showing second-order convergence and this is not the case in Babolian and Biazar (2002), where the method requires the computations of higher-order derivatives of the nonlinear operator involved in the functional equation.