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

Autor:	Alicia Cordero, Miguel A. Leonardo Sepúlveda, Juan R. Torregrosa
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	nonlinear equations iterative methods weight functions complex dynamics parameter plane basin of attraction Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Algorithms, Vol 15, Iss 10, p 387 (2022)
Druh dokumentu:	article
ISSN:	1999-4893
DOI:	10.3390/a15100387
Popis:	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.
Databáze:	Directory of Open Access Journals
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