A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case

Detalhes bibliográficos
Autor(a) principal: Gonçalves, F.F.
Data de Publicação: 2020
Outros Autores: Grossinho, Maria do Rosário, Morais, E.
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.
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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)
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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
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