Dynamics and Stability on a Family of Optimal Fourth-Order Iterative Methods

被引：9
|
作者：
Cordero, Alicia [1 ]
Leonardo Sepulveda, Miguel A. [2 ,3 ]
Torregrosa, Juan R. [1 ]
机构：
[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Camino Vera S-N, Valencia 46022, Spain
[2] Inst Tecnol Santo Domingo INTEC, Ciencias Basicas & Ambientales CBA, Area Ciencia Basica & Ambiental, Av Los Proceres,Apartado Postal 342-9 & 249-2, Santo Domingo 10602, Dominican Rep
[3] Inst Super Formac Docente Salome Urena, Dept Matemat, Recinto Felix Evaristo Mejia ISFODOSU, Av Caonabo Esq Leonardo Da Vinci, Santo Domingo 10114, Dominican Rep
来源：
ALGORITHMS | 2022年 / 15卷 / 10期
关键词：
nonlinear equations; iterative methods; weight functions; complex dynamics; parameter plane; basin of attraction; NEWTONS METHOD;
D O I：
10.3390/a15100387
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics. We obtain the fixed and critical points of the rational operator associated with the family. A stability analysis of the fixed points allows us to find sets of values of the parameter for which the behavior of the corresponding method is stable or unstable; therefore, we can select the regions of the parameter in which the methods behave more efficiently when they are applied for solving nonlinear equations or the regions in which the schemes have chaotic behavior.
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页数：13
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