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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 493707, 9 pages
http://dx.doi.org/10.1155/2012/493707
Research Article

Further Development of Jarratt Method for Solving Nonlinear Equations

Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire LS17 5JS, UK

Received 18 May 2012; Accepted 17 July 2012

Academic Editor: Michele Benzi

Copyright © 2012 R. Thukral. 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 present two new families of Jarratt-type methods for solving nonlinear equations. It is proved that the order of convergence of each family member is improved from four to six by the addition of one function evaluation. Per iteration, these new methods require two evaluations of the function and two evaluations of the first-order derivatives. In fact, the efficiency index of these methods is 1.565. Numerical comparisons are made with other existing methods to show the performance of the presented methods.