Table of Contents
Journal of Complex Analysis
Volume 2015, Article ID 259167, 9 pages
Research Article

An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics

1Department of Applied Sciences, DAV Institute of Engineering and Technology, Kabir Nagar, Jalandhar 144008, India
2Department of Mathematics, DAV College, Jalandhar 144008, India
3I.K. Gujral Punjab Technical University, Kapurthala 144601, India

Received 12 July 2015; Revised 7 October 2015; Accepted 12 October 2015

Academic Editor: Ying Hu

Copyright © 2015 Rajni Sharma and Ashu Bahl. 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.


We present a new fourth order method for finding simple roots of a nonlinear equation . In terms of computational cost, per iteration the method uses one evaluation of the function and two evaluations of its first derivative. Therefore, the method has optimal order with efficiency index 1.587 which is better than efficiency index 1.414 of Newton method and the same with Jarratt method and King’s family. Numerical examples are given to support that the method thus obtained is competitive with other similar robust methods. The conjugacy maps and extraneous fixed points of the presented method and other existing fourth order methods are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane.