Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems

[EN] A new parametric family of iterative schemes for solving nonlinear systems is presented. Fourth-order convergence is demonstrated and its stability is analyzed as a function of the parameter values. This study allows us to detect the most stable elements of the class, to find the fractals in th...

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Bibliographic Details
Authors: Cordero Barbero, Alicia|||0000-0002-7462-9173, Jordan-Lluch, Cristina|||0000-0001-9608-2984, Sanabria-Codesal, Esther|||0000-0002-4523-1991, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Format: article
Publication Date:2021
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/181023
Online Access:https://riunet.upv.es/handle/10251/181023
Access Level:Open access
Keyword:Nonlinear systems
Iterative methods
Convergence
Stability
Discrete dynamics
MATEMATICA APLICADA
Description
Summary:[EN] A new parametric family of iterative schemes for solving nonlinear systems is presented. Fourth-order convergence is demonstrated and its stability is analyzed as a function of the parameter values. This study allows us to detect the most stable elements of the class, to find the fractals in the boundary of the basins of attraction and to reject those with chaotic behavior. Some numerical tests show the performance of the new methods, confirm the theoretical results and allow to compare the proposed schemes with other known ones

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