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Journal of Applied Mathematics
Volume 2014, Article ID 817656, 17 pages
Research Article

Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations

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

Received 30 July 2013; Revised 11 January 2014; Accepted 25 February 2014; Published 11 May 2014

Academic Editor: Malgorzata Peszynska

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.


The object of the present work is to give the new class of third- and fourth-order iterative methods for solving nonlinear equations. Our proposed third-order method includes methods of Weerakoon and Fernando (2000), Homeier (2005), and Chun and Kim (2010) as particular cases. The multivariate extension of some of these methods has been also deliberated. Finally, some numerical examples are given to illustrate the performances of our proposed methods by comparing them with some well existing third- and fourth-order methods. The efficiency of our proposed fourth-order method over some fourth-order methods is also confirmed by basins of attraction.