A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.

[EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on...

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Autores: Albuquerque‐Ferreira, Augusto C., Ureña, Miguel, Ramos Calle, Higinio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/156717
Acceso en línea:http://hdl.handle.net/10366/156717
Access Level:acceso abierto
Palabra clave:Fourth-order approximations
Generalized finite difference method
ill-conditioned stars
Parallel processing
12 Matemáticas
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spelling A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.Albuquerque‐Ferreira, Augusto C.Ureña, MiguelRamos Calle, HiginioFourth-order approximationsGeneralized finite difference methodill-conditioned starsill-conditioned starsParallel processing12 Matemáticas[EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on the condition number of the matrix of derivatives. In addition, we consider a scheme implemented with parallel processing for the formation of the stars and the calculation of the derivatives. We present some examples with high gradients in irregular discretizations exaggerated on purpose, to highlight the efficiency of the proposed strategy.Wiley202420242021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/156717reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1567172026-06-07T06:28:51Z
dc.title.none.fl_str_mv A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
title A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
spellingShingle A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
Albuquerque‐Ferreira, Augusto C.
Fourth-order approximations
Generalized finite difference method
ill-conditioned stars
ill-conditioned stars
Parallel processing
12 Matemáticas
title_short A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
title_full A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
title_fullStr A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
title_full_unstemmed A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
title_sort A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
dc.creator.none.fl_str_mv Albuquerque‐Ferreira, Augusto C.
Ureña, Miguel
Ramos Calle, Higinio
author Albuquerque‐Ferreira, Augusto C.
author_facet Albuquerque‐Ferreira, Augusto C.
Ureña, Miguel
Ramos Calle, Higinio
author_role author
author2 Ureña, Miguel
Ramos Calle, Higinio
author2_role author
author
dc.subject.none.fl_str_mv Fourth-order approximations
Generalized finite difference method
ill-conditioned stars
ill-conditioned stars
Parallel processing
12 Matemáticas
topic Fourth-order approximations
Generalized finite difference method
ill-conditioned stars
ill-conditioned stars
Parallel processing
12 Matemáticas
description [EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on the condition number of the matrix of derivatives. In addition, we consider a scheme implemented with parallel processing for the formation of the stars and the calculation of the derivatives. We present some examples with high gradients in irregular discretizations exaggerated on purpose, to highlight the efficiency of the proposed strategy.
publishDate 2021
dc.date.none.fl_str_mv 2021
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/156717
url http://hdl.handle.net/10366/156717
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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