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Advances in Numerical Analysis
Volume 2011 (2011), Article ID 270903, 10 pages
http://dx.doi.org/10.1155/2011/270903
Research Article

Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

Department of Mathematics, Islamic Azad University, Zahedan Branch, 98168 Zahedan, Iran

Received 21 August 2011; Accepted 17 October 2011

Academic Editor: Michele Benzi

Copyright © 2011 F. Soleymani. 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

This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.