An Efficient Iterative Method with Order of Convergence Seven for Nonlinear Equations

In this paper, we present a modified seventh-order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives at each step. Therefore the efficiency index of the presented metho...

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Bibliographic Details
Published inApplied mechanics and materials Vol. 220-223; pp. 2574 - 2577
Main Authors Guo, Li Fang, Hu, Zhong Yong, Liang, Fang, Hu, Yun Hong
Format Journal Article
LanguageEnglish
Published Trans Tech Publications Ltd 01.01.2012
Subjects
Nonlinear Equations
Iterative Method
Newton Method
Order of Convergence
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Summary:In this paper, we present a modified seventh-order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives at each step. Therefore the efficiency index of the presented method is 1.47577 which is better than that of classical Newton’s method 1.41421. Some numerical results demonstrate the efficiency and performance of the presented method.
Bibliography:Selected papers from the 2nd International Conference on Advanced Design and Manufacturing Engineering (ADME 2012), August 16-18, 2012, Taiyuan, China
ISSN:1660-9336
1662-7482
1662-7482
DOI:10.4028/www.scientific.net/AMM.220-223.2574