Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications

[EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some kn...

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Autores: Chand, Prem B., Jain, Pankaj, Chicharro, Francisco I.|||0000-0001-9116-2870, Garrido-Saez, Neus|||0000-0002-7903-8591
Tipo de recurso: artículo
Fecha de publicación:2019
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:10251/180475
Acceso en línea:https://riunet.upv.es/handle/10251/180475
Access Level:acceso abierto
Palabra clave:Nonlinear equations
Potra-Pták method
Optimal methods
Weight function
Basin of attraction
Engineering applications
MATEMATICA APLICADA
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spelling Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its ApplicationsChand, Prem B.Jain, PankajChicharro, Francisco I.|||0000-0001-9116-2870Garrido-Saez, Neus|||0000-0002-7903-8591Nonlinear equationsPotra-Pták methodOptimal methodsWeight functionBasin of attractionEngineering applicationsMATEMATICA APLICADA[EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction.The second and third authors have been partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER/UE) and Generalitat Valenciana PROMETEO/2016/089MDPI AGEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarEscuela Politécnica Superior de AlcoyGeneralitat ValencianaAGENCIA ESTATAL DE INVESTIGACIONEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/180475reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIALGeneralitat 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:10251/1804752026-06-13T07:49:27Z
dc.title.none.fl_str_mv Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
title Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
spellingShingle Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
Chand, Prem B.
Nonlinear equations
Potra-Pták method
Optimal methods
Weight function
Basin of attraction
Engineering applications
MATEMATICA APLICADA
title_short Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
title_full Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
title_fullStr Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
title_full_unstemmed Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
title_sort Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
dc.creator.none.fl_str_mv Chand, Prem B.
Jain, Pankaj
Chicharro, Francisco I.|||0000-0001-9116-2870
Garrido-Saez, Neus|||0000-0002-7903-8591
author Chand, Prem B.
author_facet Chand, Prem B.
Jain, Pankaj
Chicharro, Francisco I.|||0000-0001-9116-2870
Garrido-Saez, Neus|||0000-0002-7903-8591
author_role author
author2 Jain, Pankaj
Chicharro, Francisco I.|||0000-0001-9116-2870
Garrido-Saez, Neus|||0000-0002-7903-8591
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
Escuela Politécnica Superior de Alcoy
Generalitat Valenciana
AGENCIA ESTATAL DE INVESTIGACION
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear equations
Potra-Pták method
Optimal methods
Weight function
Basin of attraction
Engineering applications
MATEMATICA APLICADA
topic Nonlinear equations
Potra-Pták method
Optimal methods
Weight function
Basin of attraction
Engineering applications
MATEMATICA APLICADA
description [EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-10-01
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/10251/180475
url https://riunet.upv.es/handle/10251/180475
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL
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 15.300724

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