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The Scientific World Journal
Volume 2014 (2014), Article ID 890138, 5 pages
http://dx.doi.org/10.1155/2014/890138
Research Article

A New Sixth Order Method for Nonlinear Equations in R

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 31 August 2013; Accepted 28 November 2013; Published 23 January 2014

Academic Editors: A. Favini, A. Fošner, and A. Ibeas

Copyright © 2014 Sukhjit Singh and D. K. Gupta. 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

A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered.