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Journal of Mathematics
Volume 2014, Article ID 569719, 14 pages
http://dx.doi.org/10.1155/2014/569719
Research Article

An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics

Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462051, India

Received 2 May 2014; Revised 7 August 2014; Accepted 28 August 2014; Published 15 September 2014

Academic Editor: Herbert Homeier

Copyright © 2014 Anuradha Singh and J. P. Jaiswal. 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

The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient.