On optimal fourth-order iterative methods free from second derivative and their dynamics

被引：134

作者：

Chun, Changbum ^{[2
]}

Lee, Mi Young ^{[2
]}

Neta, Beny ^{[1
]}

Dzunic, Jovana ^{[3
]}

机构：

[1] USN, Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[3] Univ Nis, Dept Math, Fac Elect Engn, Nish 18000, Serbia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

Iterative methods; Order of convergence; Rational maps; Basin of attraction; Julia sets; Conjugacy classes; SOLVING NONLINEAR EQUATIONS; ORDER;

D O I：

10.1016/j.amc.2011.12.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper new fourth order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt's family of fourth-order methods are obtained as special cases. We then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three. The basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance. Published by Elsevier Inc.

引用

页码：6427 / 6438

页数：12

共 21 条

[1]

Amat S., 2005, Aequationes Math, V69, P212

[2]

Barna B., 1956, Publ. Math. Debrecen, V4, P384

[3]

Beardon A. F., 1991, Graduate Texts in Mathematics, V132

[4] How is the dynamics of Konig iteration functions affected by their additional fixed points? [J].