Extrapolating for attaining high precision solutions for fractional partial differential equations.

[EN]This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by...

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Autores: Patrício, Fernanda Simões, Patrício, Miguel, Ramos Calle, Higinio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/157097
Acceso en línea:http://hdl.handle.net/10366/157097
Access Level:acceso abierto
Palabra clave:Fractional partial differential equations
Orthogonal polynomials
Caputo’s fractional derivative
Extrapolation process
12 Matemáticas
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spelling Extrapolating for attaining high precision solutions for fractional partial differential equations.Patrício, Fernanda SimõesPatrício, MiguelRamos Calle, HiginioFractional partial differential equationsOrthogonal polynomialsCaputo’s fractional derivativeExtrapolation process12 Matemáticas[EN]This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.Springer202420242019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/157097reponame: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:10366/1570972026-06-07T06:28:51Z
dc.title.none.fl_str_mv Extrapolating for attaining high precision solutions for fractional partial differential equations.
title Extrapolating for attaining high precision solutions for fractional partial differential equations.
spellingShingle Extrapolating for attaining high precision solutions for fractional partial differential equations.
Patrício, Fernanda Simões
Fractional partial differential equations
Orthogonal polynomials
Caputo’s fractional derivative
Extrapolation process
12 Matemáticas
title_short Extrapolating for attaining high precision solutions for fractional partial differential equations.
title_full Extrapolating for attaining high precision solutions for fractional partial differential equations.
title_fullStr Extrapolating for attaining high precision solutions for fractional partial differential equations.
title_full_unstemmed Extrapolating for attaining high precision solutions for fractional partial differential equations.
title_sort Extrapolating for attaining high precision solutions for fractional partial differential equations.
dc.creator.none.fl_str_mv Patrício, Fernanda Simões
Patrício, Miguel
Ramos Calle, Higinio
author Patrício, Fernanda Simões
author_facet Patrício, Fernanda Simões
Patrício, Miguel
Ramos Calle, Higinio
author_role author
author2 Patrício, Miguel
Ramos Calle, Higinio
author2_role author
author
dc.subject.none.fl_str_mv Fractional partial differential equations
Orthogonal polynomials
Caputo’s fractional derivative
Extrapolation process
12 Matemáticas
topic Fractional partial differential equations
Orthogonal polynomials
Caputo’s fractional derivative
Extrapolation process
12 Matemáticas
description [EN]This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.
publishDate 2019
dc.date.none.fl_str_mv 2019
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/10366/157097
url http://hdl.handle.net/10366/157097
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 Springer
publisher.none.fl_str_mv Springer
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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