Design and multidimensional extension of iterative methods for solving nonlinear problems

[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative sche...

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Detalhes bibliográficos
Autores: Artidiello, S., Vassileva, M. P., Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/103797
Acesso em linha:https://riunet.upv.es/handle/10251/103797
Access Level:acceso abierto
Palavra-chave:Nonlinear systems
Iterative method
Convergence
Efficiency index
Bratu s problem
MATEMATICA APLICADA
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spelling Design and multidimensional extension of iterative methods for solving nonlinear problemsArtidiello, S.Vassileva, M. P.Cordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Nonlinear systemsIterative methodConvergenceEfficiency indexBratu s problemMATEMATICA APLICADA[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems. The computational efficiency of the new method is compared with some known ones, obtaining good conclusions. Numerical comparisons are made with other existing methods, on standard nonlinear systems and the classical 1D-Bratu problem by transforming it in a nonlinear system by using finite differences. From this numerical examples, we confirm the theoretical results and show the performance of the presented scheme.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and FONDOCYT 2014-1C1-088 Republica Dominicana.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarMinisterio de Economía y CompetitividadFondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República DominicanaRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/103797reponame: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.Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2014-1C1-088open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1037972026-06-13T07:49:27Z
dc.title.none.fl_str_mv Design and multidimensional extension of iterative methods for solving nonlinear problems
title Design and multidimensional extension of iterative methods for solving nonlinear problems
spellingShingle Design and multidimensional extension of iterative methods for solving nonlinear problems
Artidiello, S.
Nonlinear systems
Iterative method
Convergence
Efficiency index
Bratu s problem
MATEMATICA APLICADA
title_short Design and multidimensional extension of iterative methods for solving nonlinear problems
title_full Design and multidimensional extension of iterative methods for solving nonlinear problems
title_fullStr Design and multidimensional extension of iterative methods for solving nonlinear problems
title_full_unstemmed Design and multidimensional extension of iterative methods for solving nonlinear problems
title_sort Design and multidimensional extension of iterative methods for solving nonlinear problems
dc.creator.none.fl_str_mv Artidiello, S.
Vassileva, M. P.
Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author Artidiello, S.
author_facet Artidiello, S.
Vassileva, M. P.
Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author_role author
author2 Vassileva, M. P.
Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author2_role author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Ministerio de Economía y Competitividad
Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear systems
Iterative method
Convergence
Efficiency index
Bratu s problem
MATEMATICA APLICADA
topic Nonlinear systems
Iterative method
Convergence
Efficiency index
Bratu s problem
MATEMATICA APLICADA
description [EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems. The computational efficiency of the new method is compared with some known ones, obtaining good conclusions. Numerical comparisons are made with other existing methods, on standard nonlinear systems and the classical 1D-Bratu problem by transforming it in a nonlinear system by using finite differences. From this numerical examples, we confirm the theoretical results and show the performance of the presented scheme.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
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/10251/103797
url https://riunet.upv.es/handle/10251/103797
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.
Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2014-1C1-088
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 15,300719

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