A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case
Autor(a) principal: | |
---|---|
Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/27630 |
Resumo: | We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case. |
id |
RCAP_3170dfab64bbbc40c1dbba0868d1d90a |
---|---|
oai_identifier_str |
oai:www.repository.utl.pt:10400.5/27630 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional caseCauchy ProblemParabolic PDEsUnbounded CoefficientsNon-divergent OperatorsWeighted Sobolev SpacesFinite-difference MethodsWe consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case.Academic PublicationsRepositório da Universidade de LisboaGonçalves, F.F.Grossinho, Maria do RosárioMorais, E.2023-04-14T15:51:32Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/27630engGonçalves, F.F.; Maria do Rosário Grossinho and E. Morais .(2020). “A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case”. International Journal of Applied Mathematics, Vol. 33, No. 1: pp: 137-156 : (Search PDF in 2023)1314-8060 (Online)10.12732/ijam.v33i1.11info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-04-16T01:30:44Zoai:www.repository.utl.pt:10400.5/27630Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:49:33.191574Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
title |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
spellingShingle |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case Gonçalves, F.F. Cauchy Problem Parabolic PDEs Unbounded Coefficients Non-divergent Operators Weighted Sobolev Spaces Finite-difference Methods |
title_short |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
title_full |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
title_fullStr |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
title_full_unstemmed |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
title_sort |
A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case |
author |
Gonçalves, F.F. |
author_facet |
Gonçalves, F.F. Grossinho, Maria do Rosário Morais, E. |
author_role |
author |
author2 |
Grossinho, Maria do Rosário Morais, E. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Gonçalves, F.F. Grossinho, Maria do Rosário Morais, E. |
dc.subject.por.fl_str_mv |
Cauchy Problem Parabolic PDEs Unbounded Coefficients Non-divergent Operators Weighted Sobolev Spaces Finite-difference Methods |
topic |
Cauchy Problem Parabolic PDEs Unbounded Coefficients Non-divergent Operators Weighted Sobolev Spaces Finite-difference Methods |
description |
We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 2020-01-01T00:00:00Z 2023-04-14T15:51:32Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.5/27630 |
url |
http://hdl.handle.net/10400.5/27630 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Gonçalves, F.F.; Maria do Rosário Grossinho and E. Morais .(2020). “A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case”. International Journal of Applied Mathematics, Vol. 33, No. 1: pp: 137-156 : (Search PDF in 2023) 1314-8060 (Online) 10.12732/ijam.v33i1.11 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Academic Publications |
publisher.none.fl_str_mv |
Academic Publications |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799131576299159552 |