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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 252798, 11 pages
Research Article

On Some Efficient Techniques for Solving Systems of Nonlinear Equations

1Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab 148106, India
2Department of Mathematics, Government Ranbir College, Sangrur, Punjab 148001, India

Received 18 June 2013; Revised 3 September 2013; Accepted 4 September 2013

Academic Editor: Zhangxing Chen

Copyright © 2013 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.


We present iterative methods of convergence order three, five, and six for solving systems of nonlinear equations. Third-order method is composed of two steps, namely, Newton iteration as the first step and weighted-Newton iteration as the second step. Fifth and sixth-order methods are composed of three steps of which the first two steps are same as that of the third-order method whereas the third is again a weighted-Newton step. Computational efficiency in its general form is discussed and a comparison between the efficiencies of proposed techniques with existing ones is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples. It is shown that the present methods have an edge over similar existing methods, particularly when applied to large systems of equations.