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Several New Third-Order Iterative Methods for Solving Nonlinear Equations

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Abstract

In this paper, we present some new third-order iterative methods for finding a simple root α of nonlinear scalar equation f(x)=0 in R. A geometric approach based on the circle of curvature is used to construct the new methods. Analysis of convergence shows that the new methods have third-order convergence, that is, the sequence {x n } ∞0 generated by each of the presented methods converges to α with the order of convergence three. The efficiency of the methods are tested on several numerical examples. It is observed that our methods can compete with Newton’s method and the classical third-order methods.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    Changbum Chun

  2. School of Liberal Arts, Korea University of Technology and Education, Cheonan, Chungnam, 330-708, Republic of Korea

    Yong-Il Kim

Authors
  1. Changbum Chun
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  2. Yong-Il Kim
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Correspondence to Changbum Chun.

Additional information

This paper was supported by Faculty Research Fund, Sungkyunkwan University, 2008.

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Chun, C., Kim, YI. Several New Third-Order Iterative Methods for Solving Nonlinear Equations. Acta Appl Math 109, 1053–1063 (2010). https://doi.org/10.1007/s10440-008-9359-3

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  • DOI: https://doi.org/10.1007/s10440-008-9359-3

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