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

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 analys...

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Bibliographic Details
Published inAlgorithms Vol. 15; no. 10; p. 387
Main Authors Cordero, Alicia, Leonardo Sepúlveda, Miguel A., Torregrosa, Juan R.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2022
Subjects
basin of attraction
complex dynamics
Complex systems
Convergence (Mathematics)
Critical point
Dynamic stability
Efficiency
Fixed point theory
Iterative methods
Iterative methods (Mathematics)
Methods
Nonlinear equations
Orbits
parameter plane
Parameters
Stability
Stability analysis
weight functions
Spain
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Summary: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.
ISSN:1999-4893
1999-4893
DOI:10.3390/a15100387