Abstract and Applied Analysis

A New Second-Order Iteration Method for Solving Nonlinear Equations

Shin Min Kang, Arif Rafiq, and Young Chel Kwun

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Abstract

We establish a new second-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.4142 which is the same as the Newton-Raphson method. By using some examples, the efficiency of the method is also discussed. It is worth to note that (i) our method is performing very well in comparison to the fixed point method and the method discussed in Babolian and Biazar (2002) and (ii) our method is so simple to apply in comparison to the method discussed in Babolian and Biazar (2002) and involves only first-order derivative but showing second-order convergence and this is not the case in Babolian and Biazar (2002), where the method requires the computations of higher-order derivatives of the nonlinear operator involved in the functional equation.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 487062, 4 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450430

Digital Object Identifier
doi:10.1155/2013/487062

Mathematical Reviews number (MathSciNet)
MR3044900

Zentralblatt MATH identifier
1343.65055

Citation

Kang, Shin Min; Rafiq, Arif; Kwun, Young Chel. A New Second-Order Iteration Method for Solving Nonlinear Equations. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 487062, 4 pages. doi:10.1155/2013/487062. https://projecteuclid.org/euclid.aaa/1393450430


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