Several New Third-Order Iterative Methods for Solving Nonlinear Equations

被引：0
|
作者：
Changbum Chun
Yong-Il Kim
机构：
[1] Sungkyunkwan University,Department of Mathematics
[2] Korea University of Technology and Education,School of Liberal Arts
来源：
Acta Applicandae Mathematicae | 2010年 / 109卷
关键词：
Newton’s method; Iterative methods; Nonlinear equations; Order of convergence; Circle of curvature; Efficiency index; 41A25; 65D99;
D O I：
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中图分类号：
学科分类号：
摘要：
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 {xn}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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页码：1053 / 1063
页数：10
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