High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems

The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be...

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Detalles Bibliográficos
Autores: Gonz´alez-Pinto, Severiano, Hairer, E., Hernández Abreu, Domingo
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad de La Laguna (ULL)
Repositorio:RIULL. Repositorio Institucional de la Universidad de La Laguna
OAI Identifier:oai:riull.ull.es:915/39034
Acceso en línea:http://riull.ull.es/xmlui/handle/915/39034
Access Level:acceso abierto
Palabra clave:Parabolic problem
AMF-W method
PDE-convergence
Order conditions
Fractional order
AMS subject classifications: 65M12, 65M15, 65M20
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spelling High order PDE-convergence of AMF-W methods for 2D-linear parabolic problemsGonz´alez-Pinto, SeverianoHairer, E.Hernández Abreu, DomingoParabolic problemAMF-W methodPDE-convergenceOrder conditionsFractional orderAMS subject classifications: 65M12, 65M15, 65M20The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be sufficient for PDE-convergence of order p (independently of the spatial resolution) in the case of time-independent Dirichlet boundary conditions. Under additional conditions, PDE-convergence of order p = 3.25 − for every > 0 can be obtained. In the case of time-dependent boundary conditions the order reduction is more dramatic, but order p = 2.25 − for every > 0 can be achieved.Análisis MatemáticoGrupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/202420242022info:eu-repo/semantics/articleapplication/pdfhttp://riull.ull.es/xmlui/handle/915/39034reponame:RIULL. Repositorio Institucional de la Universidad de La Lagunainstname:Universidad de La Laguna (ULL)InglésLicencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ESoai:riull.ull.es:915/390342026-06-22T13:13:57Z
dc.title.none.fl_str_mv High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
title High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
spellingShingle High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
Gonz´alez-Pinto, Severiano
Parabolic problem
AMF-W method
PDE-convergence
Order conditions
Fractional order
AMS subject classifications: 65M12, 65M15, 65M20
title_short High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
title_full High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
title_fullStr High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
title_full_unstemmed High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
title_sort High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
dc.creator.none.fl_str_mv Gonz´alez-Pinto, Severiano
Hairer, E.
Hernández Abreu, Domingo
author Gonz´alez-Pinto, Severiano
author_facet Gonz´alez-Pinto, Severiano
Hairer, E.
Hernández Abreu, Domingo
author_role author
author2 Hairer, E.
Hernández Abreu, Domingo
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
Grupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
dc.subject.none.fl_str_mv Parabolic problem
AMF-W method
PDE-convergence
Order conditions
Fractional order
AMS subject classifications: 65M12, 65M15, 65M20
topic Parabolic problem
AMF-W method
PDE-convergence
Order conditions
Fractional order
AMS subject classifications: 65M12, 65M15, 65M20
description The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be sufficient for PDE-convergence of order p (independently of the spatial resolution) in the case of time-independent Dirichlet boundary conditions. Under additional conditions, PDE-convergence of order p = 3.25 − for every > 0 can be obtained. In the case of time-dependent boundary conditions the order reduction is more dramatic, but order p = 2.25 − for every > 0 can be achieved.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://riull.ull.es/xmlui/handle/915/39034
url http://riull.ull.es/xmlui/handle/915/39034
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
rights_invalid_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIULL. Repositorio Institucional de la Universidad de La Laguna
instname:Universidad de La Laguna (ULL)
instname_str Universidad de La Laguna (ULL)
reponame_str RIULL. Repositorio Institucional de la Universidad de La Laguna
collection RIULL. Repositorio Institucional de la Universidad de La Laguna
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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