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International Journal of Engineering Mathematics
Volume 2014 (2014), Article ID 828409, 11 pages
http://dx.doi.org/10.1155/2014/828409
Research Article

Several New Third-Order and Fourth-Order Iterative Methods for Solving Nonlinear Equations

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

Received 17 August 2013; Revised 12 December 2013; Accepted 31 December 2013; Published 23 February 2014

Academic Editor: Viktor Popov

Copyright © 2014 Anuradha Singh and 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

In order to find the zeros of nonlinear equations, in this paper, we propose a family of third-order and optimal fourth-order iterative methods. We have also obtained some particular cases of these methods. These methods are constructed through weight function concept. The multivariate case of these methods has also been discussed. The numerical results show that the proposed methods are more efficient than some existing third- and fourth-order methods.