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Advances in Numerical Analysis
Volume 2014 (2014), Article ID 963878, 8 pages
http://dx.doi.org/10.1155/2014/963878
Research Article

General Family of Third Order Methods for Multiple Roots of Nonlinear Equations and Basin Attractors for Various Methods

1Department of Applied Sciences, D.A.V. Institute of Engineering and Technology, Kabir Nagar, Jalandhar 144008, India
2Department of Mathematics, D.A.V. College, Jalandhar 144008, India

Received 29 November 2013; Accepted 8 February 2014; Published 31 March 2014

Academic Editor: Ting-Zhu Huang

Copyright © 2014 Rajni Sharma and Ashu Bahl. 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

A general scheme of third order convergence is described for finding multiple roots of nonlinear equations. The proposed scheme requires one evaluation of , and each per iteration and contains several known one-point third order methods for finding multiple roots, as particular cases. Numerical examples are included to confirm the theoretical results and demonstrate convergence behavior of the proposed methods. In the end, we provide the basins of attraction for some methods to observe their dynamics in the complex plane.