Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy

A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded paramete...

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Detalles Bibliográficos
Autores: Qasim, Uswah, Ali, Zulifgar, Ahmad, Fayyaz, Serra Capizzano, Stefano, Ullah, Malik Zaka, Asma, Mir
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/100357
Acceso en línea:https://hdl.handle.net/2117/100357
https://dx.doi.org/10.3390/a9010018
Access Level:acceso abierto
Palabra clave:Iterative methods (Mathematics)
systems of nonlinear equations
frozen Jacobian
ordinary differential equations
partial differential equations
homotopy method
DIFFERENTIAL-EQUATIONS
DECOMPOSITION METHOD
NUMERICAL-SOLUTION
NEWTONS METHOD
Mètodes iteratius (Matemàtica)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
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spelling Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopyQasim, UswahAli, ZulifgarAhmad, FayyazSerra Capizzano, StefanoUllah, Malik ZakaAsma, MirIterative methods (Mathematics)systems of nonlinear equationsfrozen Jacobianordinary differential equationspartial differential equationshomotopy methodDIFFERENTIAL-EQUATIONSDECOMPOSITION METHODNUMERICAL-SOLUTIONNEWTONS METHODMètodes iteratius (Matemàtica)Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàticaA homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.Peer Reviewed20162016-03-0120172017-01-31journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/100357https://dx.doi.org/10.3390/a9010018reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1003572026-05-27T15:37:01Z
dc.title.none.fl_str_mv Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
title Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
spellingShingle Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
Qasim, Uswah
Iterative methods (Mathematics)
systems of nonlinear equations
frozen Jacobian
ordinary differential equations
partial differential equations
homotopy method
DIFFERENTIAL-EQUATIONS
DECOMPOSITION METHOD
NUMERICAL-SOLUTION
NEWTONS METHOD
Mètodes iteratius (Matemàtica)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
title_short Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
title_full Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
title_fullStr Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
title_full_unstemmed Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
title_sort Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
dc.creator.none.fl_str_mv Qasim, Uswah
Ali, Zulifgar
Ahmad, Fayyaz
Serra Capizzano, Stefano
Ullah, Malik Zaka
Asma, Mir
author Qasim, Uswah
author_facet Qasim, Uswah
Ali, Zulifgar
Ahmad, Fayyaz
Serra Capizzano, Stefano
Ullah, Malik Zaka
Asma, Mir
author_role author
author2 Ali, Zulifgar
Ahmad, Fayyaz
Serra Capizzano, Stefano
Ullah, Malik Zaka
Asma, Mir
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Iterative methods (Mathematics)
systems of nonlinear equations
frozen Jacobian
ordinary differential equations
partial differential equations
homotopy method
DIFFERENTIAL-EQUATIONS
DECOMPOSITION METHOD
NUMERICAL-SOLUTION
NEWTONS METHOD
Mètodes iteratius (Matemàtica)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
topic Iterative methods (Mathematics)
systems of nonlinear equations
frozen Jacobian
ordinary differential equations
partial differential equations
homotopy method
DIFFERENTIAL-EQUATIONS
DECOMPOSITION METHOD
NUMERICAL-SOLUTION
NEWTONS METHOD
Mètodes iteratius (Matemàtica)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
description A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-03-01
2017
2017-01-31
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://hdl.handle.net/2117/100357
https://dx.doi.org/10.3390/a9010018
url https://hdl.handle.net/2117/100357
https://dx.doi.org/10.3390/a9010018
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869411692891340800
score 15,301603

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