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

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

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 bou...

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Main Authors: Alicia Cordero, Cristina Jordán, Esther Sanabria-Codesal, Juan R. Torregrosa
Format: Article
Language:English
Published: MDPI AG 2021-09-01
Series:Fractal and Fractional
Subjects:
nonlinear systems
iterative methods
convergence
stability
discrete dynamics
Online Access:https://www.mdpi.com/2504-3110/5/3/125
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spelling doaj-92e5f22523e44ec78fd297b65fc99a3e2021-09-26T00:11:29ZengMDPI AGFractal and Fractional2504-31102021-09-01512512510.3390/fractalfract5030125Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial ProblemsAlicia Cordero0Cristina Jordán1Esther Sanabria-Codesal2Juan R. Torregrosa3Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainDepartment of Applied Mathematics, Universitat Politècnica de València, 46022 València, SpainInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainA 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.https://www.mdpi.com/2504-3110/5/3/125nonlinear systemsiterative methodsconvergencestabilitydiscrete dynamics
collection DOAJ
language English
format Article
sources DOAJ
author Alicia Cordero
Cristina Jordán
Esther Sanabria-Codesal
Juan R. Torregrosa
spellingShingle Alicia Cordero
Cristina Jordán
Esther Sanabria-Codesal
Juan R. Torregrosa
Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
Fractal and Fractional
nonlinear systems
iterative methods
convergence
stability
discrete dynamics
author_facet Alicia Cordero
Cristina Jordán
Esther Sanabria-Codesal
Juan R. Torregrosa
author_sort Alicia Cordero
title Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
title_short Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
title_full Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
title_fullStr Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
title_full_unstemmed Design, Convergence and Stability of a Fourth-Order Class of Iterative Methods for Solving Nonlinear Vectorial Problems
title_sort design, convergence and stability of a fourth-order class of iterative methods for solving nonlinear vectorial problems
publisher MDPI AG
series Fractal and Fractional
issn 2504-3110
publishDate 2021-09-01
description 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.
topic nonlinear systems
iterative methods
convergence
stability
discrete dynamics
url https://www.mdpi.com/2504-3110/5/3/125
work_keys_str_mv AT aliciacordero designconvergenceandstabilityofafourthorderclassofiterativemethodsforsolvingnonlinearvectorialproblems
AT cristinajordan designconvergenceandstabilityofafourthorderclassofiterativemethodsforsolvingnonlinearvectorialproblems
AT esthersanabriacodesal designconvergenceandstabilityofafourthorderclassofiterativemethodsforsolvingnonlinearvectorialproblems
AT juanrtorregrosa designconvergenceandstabilityofafourthorderclassofiterativemethodsforsolvingnonlinearvectorialproblems
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