Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt

[EN] It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth order schemes (extended to the case of several variables) are employed as starting steps in order to design higher order m...

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Jordan-Lluch, Cristina|||0000-0001-9608-2984, Sanabria-Codesal, Esther|||0000-0002-4523-1991, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Tipo de recurso: artículo
Fecha de publicación:2018
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:10251/121415
Acceso en línea:https://riunet.upv.es/handle/10251/121415
Access Level:acceso abierto
Palabra clave:Nonlinear systems
Iterative method
Convergence
Efficiency index
Fisher&apos
s equation
MATEMATICA APLICADA
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spelling Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt5Cordero Barbero, Alicia|||0000-0002-7462-9173Jordan-Lluch, Cristina|||0000-0001-9608-2984Sanabria-Codesal, Esther|||0000-0002-4523-1991Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Nonlinear systemsIterative methodConvergenceEfficiency indexFisher&aposs equationMATEMATICA APLICADA[EN] It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth order schemes (extended to the case of several variables) are employed as starting steps in order to design higher order methods for this kind of problems. In this paper, we use a non optimal (in scalar case) iterative procedure that is specially efficient for solving nonlinear systems, as the initial steps of an eighth-order scheme that improves the computational efficiency indices of the existing methods, as far as the authors know. Moreover, the method can be modified by adding similar steps, increasing the order of convergence three times per step added. This kind of procedures can be used for solving big-sized problems, such as those obtained by applying finite differences for approximating the solution of diffusion problem, heat conduction equations, etc. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and Fisher's equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the proposed schemes. (C) 2017 Elsevier B.V. All rights reserved.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P, MTM2015-64013-P and Generalitat Valenciana PROMETEO/2016/089.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería InformáticaGeneralitat ValencianaMinisterio de Economía y CompetitividadMinisterio de Economía, Industria y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/121415reponame: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 MTM2015-64013-P SINGULARIDADES, GEOMETRIA GENERICA Y APLICACIONESMinisterio 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 - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1214152026-06-13T07:49:27Z
dc.title.none.fl_str_mv Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
5
title Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
spellingShingle Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
Cordero Barbero, Alicia|||0000-0002-7462-9173
Nonlinear systems
Iterative method
Convergence
Efficiency index
Fisher&apos
s equation
MATEMATICA APLICADA
title_short Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
title_full Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
title_fullStr Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
title_full_unstemmed Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
title_sort Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p&gt
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Jordan-Lluch, Cristina|||0000-0001-9608-2984
Sanabria-Codesal, Esther|||0000-0002-4523-1991
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author Cordero Barbero, Alicia|||0000-0002-7462-9173
author_facet Cordero Barbero, Alicia|||0000-0002-7462-9173
Jordan-Lluch, Cristina|||0000-0001-9608-2984
Sanabria-Codesal, Esther|||0000-0002-4523-1991
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
author_role author
author2 Jordan-Lluch, Cristina|||0000-0001-9608-2984
Sanabria-Codesal, Esther|||0000-0002-4523-1991
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
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Informática
Generalitat Valenciana
Ministerio de Economía y Competitividad
Ministerio de Economía, Industria y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear systems
Iterative method
Convergence
Efficiency index
Fisher&apos
s equation
MATEMATICA APLICADA
topic Nonlinear systems
Iterative method
Convergence
Efficiency index
Fisher&apos
s equation
MATEMATICA APLICADA
description [EN] It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth order schemes (extended to the case of several variables) are employed as starting steps in order to design higher order methods for this kind of problems. In this paper, we use a non optimal (in scalar case) iterative procedure that is specially efficient for solving nonlinear systems, as the initial steps of an eighth-order scheme that improves the computational efficiency indices of the existing methods, as far as the authors know. Moreover, the method can be modified by adding similar steps, increasing the order of convergence three times per step added. This kind of procedures can be used for solving big-sized problems, such as those obtained by applying finite differences for approximating the solution of diffusion problem, heat conduction equations, etc. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and Fisher's equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the proposed schemes. (C) 2017 Elsevier B.V. All rights reserved.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
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/10251/121415
url https://riunet.upv.es/handle/10251/121415
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 MTM2015-64013-P SINGULARIDADES, GEOMETRIA GENERICA Y APLICACIONES
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 - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/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 - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
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 15,300724

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