Construction of fourth-order optimal families of iterative methods and their dynamics

[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without memory for obtaining simple roots. This class requires only three functional evaluations (viz. two evaluations of function f(xn), f(yn) and one of its first-order derivative f (xn)) per iteration. Furt...

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Detalles Bibliográficos
Autores: Behl, Ramandeep, Motsa, Sandile S., Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/64679
Acceso en línea:https://riunet.upv.es/handle/10251/64679
Access Level:acceso abierto
Palabra clave:Nonlinear equations
Iterative methods
Optimal order of convergence
Complex dynamics
Parameter plane
Basin of attraction
MATEMATICA APLICADA
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spelling Construction of fourth-order optimal families of iterative methods and their dynamicsBehl, RamandeepMotsa, Sandile S.Cordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Nonlinear equationsIterative methodsOptimal order of convergenceComplex dynamicsParameter planeBasin of attractionMATEMATICA APLICADA[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without memory for obtaining simple roots. This class requires only three functional evaluations (viz. two evaluations of function f(xn), f(yn) and one of its first-order derivative f (xn)) per iteration. Further, we show that the well-known Ostrowski’s method and King’s family of fourth-order procedures are special cases of our proposed schemes. One of the new particular subclasses is a biparametric family of iterative methods. By using complex dynamics tools, its stability is analyzed, showing stable members of the family. Further on, one of the parameters is fixed and the stability of the resulting class is studied. On the other hand, the accuracy and validity of new schemes is tested by a number of numerical examples by comparing them with recent and classical optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C02-02.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-11-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/64679reponame: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 MATRICIALESopen 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:10251/646792026-06-13T07:49:27Z
dc.title.none.fl_str_mv Construction of fourth-order optimal families of iterative methods and their dynamics
title Construction of fourth-order optimal families of iterative methods and their dynamics
spellingShingle Construction of fourth-order optimal families of iterative methods and their dynamics
Behl, Ramandeep
Nonlinear equations
Iterative methods
Optimal order of convergence
Complex dynamics
Parameter plane
Basin of attraction
MATEMATICA APLICADA
title_short Construction of fourth-order optimal families of iterative methods and their dynamics
title_full Construction of fourth-order optimal families of iterative methods and their dynamics
title_fullStr Construction of fourth-order optimal families of iterative methods and their dynamics
title_full_unstemmed Construction of fourth-order optimal families of iterative methods and their dynamics
title_sort Construction of fourth-order optimal families of iterative methods and their dynamics
dc.creator.none.fl_str_mv Behl, Ramandeep
Motsa, Sandile S.
Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author Behl, Ramandeep
author_facet Behl, Ramandeep
Motsa, Sandile S.
Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author_role author
author2 Motsa, Sandile S.
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
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear equations
Iterative methods
Optimal order of convergence
Complex dynamics
Parameter plane
Basin of attraction
MATEMATICA APLICADA
topic Nonlinear equations
Iterative methods
Optimal order of convergence
Complex dynamics
Parameter plane
Basin of attraction
MATEMATICA APLICADA
description [EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without memory for obtaining simple roots. This class requires only three functional evaluations (viz. two evaluations of function f(xn), f(yn) and one of its first-order derivative f (xn)) per iteration. Further, we show that the well-known Ostrowski’s method and King’s family of fourth-order procedures are special cases of our proposed schemes. One of the new particular subclasses is a biparametric family of iterative methods. By using complex dynamics tools, its stability is analyzed, showing stable members of the family. Further on, one of the parameters is fixed and the stability of the resulting class is studied. On the other hand, the accuracy and validity of new schemes is tested by a number of numerical examples by comparing them with recent and classical optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-11-15
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/10251/64679
url https://riunet.upv.es/handle/10251/64679
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
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 15,301603

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