Several New Third-Order Iterative Methods for Solving Nonlinear Equations

被引：22
|
作者：
Chun, Changbum [1 ]
Kim, Yong-Il [2 ]
机构：
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[2] Korea Univ Technol & Educ, Sch Liberal Arts, Cheonan 330708, Chungnam, South Korea
来源：
ACTA APPLICANDAE MATHEMATICAE | 2010年 / 109卷 / 03期
关键词：
Newton's method; Iterative methods; Nonlinear equations; Order of convergence; Circle of curvature; Efficiency index; NEWTONS METHOD; HALLEY; FAMILY; VARIANTS;
D O I：
10.1007/s10440-008-9359-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present some new third-order iterative methods for finding a simple root a 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)(infinity) generated by each of the presented methods converges to a 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：11
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