Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations

[EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra-Ptak method and last is weighted-Newton step. Furthermore, we generalize ou...

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Authors: Arora, Himani, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Cordero Barbero, Alicia|||0000-0002-7462-9173
Format: article
Publication Date:2019
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:10251/159334
Online Access:https://riunet.upv.es/handle/10251/159334
Access Level:Open access
Keyword:Systems of nonlinear equations
Iterative methods
Newton&apos
s method
Order of convergence
Computational efficiency
Basin of attraction
MATEMATICA APLICADA
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spelling Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equationsArora, HimaniTorregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Cordero Barbero, Alicia|||0000-0002-7462-9173Systems of nonlinear equationsIterative methodsNewton&aposs methodOrder of convergenceComputational efficiencyBasin of attractionMATEMATICA APLICADA[EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra-Ptak method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3r + 6, r = 0, 1, 2, .... The sixth order method is the special case of this multi-step scheme for r = 0. The family gives a four-step ninth order method for r = 1. As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.This research was partially supported by Ministerio de Economia y Competitividad under grants MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.MDPI AGEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-03-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/159334reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-52016-C2-2-P DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES.Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2016%2F089 Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicacionesopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1593342026-06-13T07:49:27Z
dc.title.none.fl_str_mv Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
title Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
spellingShingle Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
Arora, Himani
Systems of nonlinear equations
Iterative methods
Newton&apos
s method
Order of convergence
Computational efficiency
Basin of attraction
MATEMATICA APLICADA
title_short Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
title_full Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
title_fullStr Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
title_full_unstemmed Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
title_sort Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
dc.creator.none.fl_str_mv Arora, Himani
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Cordero Barbero, Alicia|||0000-0002-7462-9173
author Arora, Himani
author_facet Arora, Himani
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Cordero Barbero, Alicia|||0000-0002-7462-9173
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Cordero Barbero, Alicia|||0000-0002-7462-9173
author2_role author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Generalitat Valenciana
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Systems of nonlinear equations
Iterative methods
Newton&apos
s method
Order of convergence
Computational efficiency
Basin of attraction
MATEMATICA APLICADA
topic Systems of nonlinear equations
Iterative methods
Newton&apos
s method
Order of convergence
Computational efficiency
Basin of attraction
MATEMATICA APLICADA
description [EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra-Ptak method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3r + 6, r = 0, 1, 2, .... The sixth order method is the special case of this multi-step scheme for r = 0. The family gives a four-step ninth order method for r = 1. As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/159334
url https://riunet.upv.es/handle/10251/159334
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-52016-C2-2-P DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES.
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2016%2F089 Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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