On Some Efficient Techniques for Solving Systems of Nonlinear Equations. (31st October 2013)

• Record Type: Journal Article
• Authors: Sharma, Janak Raj; Gupta, Puneet
• Other Names: Chen Zhangxing Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2013(2013)
• Publication Date: 2013-10-31
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2013/252798
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : 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.