A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions

[EN] Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the o...

Descripción completa

Detalles Bibliográficos
Autores: Chang, Chih-Wen, Qureshi, Sania, Argyros, Ioannis K., Soomro, Amanullah, Chicharro, Francisco I.|||0000-0001-9116-2870
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::be2e213d4202096392f4b0c51734dcf8
Acceso en línea:https://riunet.upv.es/handle/10251/234019
Access Level:acceso embargado
Palabra clave:Root-finding methods
Nonlinear models
Iterative algorithms
Efficiency index
Computational order of convergence
Computational cost
id ES_f318ef16aa4e2b1a62202dda69e2ce47
oai_identifier_str oai:dnet:riunet______::be2e213d4202096392f4b0c51734dcf8
network_acronym_str ES
network_name_str España
repository_id_str
spelling A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensionsChang, Chih-WenQureshi, SaniaArgyros, Ioannis K.Soomro, AmanullahChicharro, Francisco I.|||0000-0001-9116-2870Root-finding methodsNonlinear modelsIterative algorithmsEfficiency indexComputational order of convergenceComputational cost[EN] Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the optimal convergence, adhering to the Kung-Traub conjecture, and necessitates only three function evaluations per iteration to achieve a fourth-order optimal iterative process. The development of this method involves the amalgamation of two well-established third-order iterative techniques. Comprehensive local and semilocal convergence analyses are conducted, accompanied by a stability investigation of the proposed approach. This method marks a substantial enhancement over existing optimal iterative methods, as evidenced by its performance in various nonlinear models. Extensive testing demonstrates that the proposed method consistently yields accurate and efficient results, surpassing existing algorithms in both speed and accuracy. Numerical simulations, including real-world models such as boundary value problems and integral equations, indicate that the proposed optimal method outperforms several contemporary optimal iterative techniques.This work was financially supported by the National Science and Technology Council, Taiwan [grant numbers: NSTC 112-2221- E-239-022]. This study has been partially funded to F.I.C. by Ayuda a Primeros Proyectos de Investigación, Spain (PAID-06-23), Vicerrectorado de Investigación de la Universitat Politècnica de València (UPV) , in the framework of project MERLIN.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarUNIVERSIDAD POLITECNICA DE VALENCIANational Science and Technology Council, TaiwanRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-03-0120262026-04-0120262026-10-31journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/234019reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengUPV-VIN UPV-VIN PAID-06-23 Mejora de la Eficiencia en la Resolución de problemas no LINeales (MERLIN)NSTC NSTC 112-2221-E-239-022embargoed accesshttp://purl.org/coar/access_right/c_f1cfReconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/embargoedAccessoai:dnet:riunet______::be2e213d4202096392f4b0c51734dcf82026-06-13T07:49:27Z
dc.title.none.fl_str_mv A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
title A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
spellingShingle A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
Chang, Chih-Wen
Root-finding methods
Nonlinear models
Iterative algorithms
Efficiency index
Computational order of convergence
Computational cost
title_short A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
title_full A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
title_fullStr A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
title_full_unstemmed A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
title_sort A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions
dc.creator.none.fl_str_mv Chang, Chih-Wen
Qureshi, Sania
Argyros, Ioannis K.
Soomro, Amanullah
Chicharro, Francisco I.|||0000-0001-9116-2870
author Chang, Chih-Wen
author_facet Chang, Chih-Wen
Qureshi, Sania
Argyros, Ioannis K.
Soomro, Amanullah
Chicharro, Francisco I.|||0000-0001-9116-2870
author_role author
author2 Qureshi, Sania
Argyros, Ioannis K.
Soomro, Amanullah
Chicharro, Francisco I.|||0000-0001-9116-2870
author2_role author
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
UNIVERSIDAD POLITECNICA DE VALENCIA
National Science and Technology Council, Taiwan
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Root-finding methods
Nonlinear models
Iterative algorithms
Efficiency index
Computational order of convergence
Computational cost
topic Root-finding methods
Nonlinear models
Iterative algorithms
Efficiency index
Computational order of convergence
Computational cost
description [EN] Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the optimal convergence, adhering to the Kung-Traub conjecture, and necessitates only three function evaluations per iteration to achieve a fourth-order optimal iterative process. The development of this method involves the amalgamation of two well-established third-order iterative techniques. Comprehensive local and semilocal convergence analyses are conducted, accompanied by a stability investigation of the proposed approach. This method marks a substantial enhancement over existing optimal iterative methods, as evidenced by its performance in various nonlinear models. Extensive testing demonstrates that the proposed method consistently yields accurate and efficient results, surpassing existing algorithms in both speed and accuracy. Numerical simulations, including real-world models such as boundary value problems and integral equations, indicate that the proposed optimal method outperforms several contemporary optimal iterative techniques.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-03-01
2026
2026-04-01
2026
2026-10-31
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/10251/234019
url https://riunet.upv.es/handle/10251/234019
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv UPV-VIN UPV-VIN PAID-06-23 Mejora de la Eficiencia en la Resolución de problemas no LINeales (MERLIN)
NSTC NSTC 112-2221-E-239-022
dc.rights.none.fl_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
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/embargoedAccess
rights_invalid_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv embargoedAccess
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
_version_ 1869424344542740480
score 15,81155

Similares en LA Referencia