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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 795628, 6 pages
http://dx.doi.org/10.1155/2014/795628
Research Article

Solving Nondifferentiable Nonlinear Equations by New Steffensen-Type Iterative Methods with Memory

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

Received 5 August 2014; Revised 15 November 2014; Accepted 26 November 2014; Published 21 December 2014

Academic Editor: Alessandro Palmeri

Copyright © 2014 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

It is attempted to present two derivative-free Steffensen-type methods with memory for solving nonlinear equations. By making use of a suitable self-accelerator parameter in the existing optimal fourth- and eighth-order without memory methods, the order of convergence has been increased without any extra function evaluation. Therefore, its efficiency index is also increased, which is the main contribution of this paper. The self-accelerator parameters are estimated using Newton’s interpolation. To show applicability of the proposed methods, some numerical illustrations are presented.