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Advances in Numerical Analysis
Volume 2014 (2014), Article ID 152187, 11 pages
Research Article

An Efficient Family of Traub-Steffensen-Type Methods for Solving Systems of Nonlinear Equations

1Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab 148 106, India
2Department of Mathematics, Government Ranbir College, Sangrur, Punjab 148 001, India

Received 6 February 2014; Accepted 11 June 2014; Published 2 July 2014

Academic Editor: Zhangxin Chen

Copyright © 2014 Janak Raj Sharma and Puneet Gupta. 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.


Based on Traub-Steffensen method, we present a derivative free three-step family of sixth-order methods for solving systems of nonlinear equations. The local convergence order of the family is determined using first-order divided difference operator for functions of several variables and direct computation by Taylor's expansion. Computational efficiency is discussed, and a comparison between the efficiencies of the proposed techniques with the existing ones is made. Numerical tests are performed to compare the methods of the proposed family with the existing methods and to confirm the theoretical results. It is shown that the new family is especially efficient in solving large systems.