Complex dynamics of derivative-free methods for nonlinear equations

被引：88

作者：

Chicharro, Francisco ^{[1
]}

Cordero, Alicia ^{[1
]}

Gutierrez, Jose M. ^{[2
]}

Torregrosa, Juan R. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia, Spain

[2] Univ la Rioja, Dept Matemat & Comp, Logrono, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 12期

关键词：

Nonlinear equation; Iterative method; Derivative-free method; Complex dynamics; Parameters plane; Fixed point; Critical point; Immersed basin of attraction; ITERATIVE METHODS;

D O I：

10.1016/j.amc.2012.12.075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. Different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients. The property of immersion of the basins of attraction in all cases is analyzed. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：7023 / 7035

页数：13

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