Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 697642, 6 pages
http://dx.doi.org/10.1155/2014/697642
Research Article

Potra-Pták Iterative Method with Memory

1Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran
2Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 8 September 2013; Accepted 5 November 2013; Published 22 January 2014

Academic Editors: I. Straškraba and C. Zhu

Copyright © 2014 Taher Lotfi 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

The problem is to extend the method proposed by Soleymani et al. (2012) to a method with memory. Following this aim, a free parameter is calculated using Newton’s interpolatory polynomial of the third degree. So the R-order of convergence is increased from 4 to 6 without any new function evaluations. Numerically the extended method is examined along with comparison to some existing methods with the similar properties.