Journal of Applied Mathematics
Volume 2012 (2012), Article ID 282561, 9 pages
http://dx.doi.org/10.1155/2012/282561
Research Article

A Family of Iterative Methods with Accelerated Eighth-Order Convergence

Alicia Cordero,1 Mojtaba Fardi,2 Mehdi Ghasemi,3 and Juan R. Torregrosa1

1Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain
2Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran
3Department of Applied Mathematics, Faculty of Basic Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

Received 15 June 2012; Revised 24 July 2012; Accepted 26 July 2012

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2012 Alicia Cordero 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 propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorithms with known ones and confirm the theoretical results.