A pseudospectral method for the one-dimensional fractional Laplacian on R

In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as...

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Detalhes bibliográficos
Autores: Cayama, J., Cuesta, C.M., De la Hoz, F.
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1453
Acesso em linha:http://hdl.handle.net/20.500.11824/1453
Access Level:acceso abierto
Palavra-chave:Accelerating fronts
Fractional Laplacian
Nonlocal Fisher's equation
Pseudospectral methods
Rational Chebyshev functions
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spelling A pseudospectral method for the one-dimensional fractional Laplacian on RCayama, J.Cuesta, C.M.De la Hoz, F.Accelerating frontsFractional LaplacianNonlocal Fisher's equationPseudospectral methodsRational Chebyshev functionsIn this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function. As an application of the method, we also do the simulation of Fisher's equation with fractional Laplacian in the monostable case.202220222021info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1453reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/669689Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/14532026-06-19T12:47:47Z
dc.title.none.fl_str_mv A pseudospectral method for the one-dimensional fractional Laplacian on R
title A pseudospectral method for the one-dimensional fractional Laplacian on R
spellingShingle A pseudospectral method for the one-dimensional fractional Laplacian on R
Cayama, J.
Accelerating fronts
Fractional Laplacian
Nonlocal Fisher's equation
Pseudospectral methods
Rational Chebyshev functions
title_short A pseudospectral method for the one-dimensional fractional Laplacian on R
title_full A pseudospectral method for the one-dimensional fractional Laplacian on R
title_fullStr A pseudospectral method for the one-dimensional fractional Laplacian on R
title_full_unstemmed A pseudospectral method for the one-dimensional fractional Laplacian on R
title_sort A pseudospectral method for the one-dimensional fractional Laplacian on R
dc.creator.none.fl_str_mv Cayama, J.
Cuesta, C.M.
De la Hoz, F.
author Cayama, J.
author_facet Cayama, J.
Cuesta, C.M.
De la Hoz, F.
author_role author
author2 Cuesta, C.M.
De la Hoz, F.
author2_role author
author
dc.subject.none.fl_str_mv Accelerating fronts
Fractional Laplacian
Nonlocal Fisher's equation
Pseudospectral methods
Rational Chebyshev functions
topic Accelerating fronts
Fractional Laplacian
Nonlocal Fisher's equation
Pseudospectral methods
Rational Chebyshev functions
description In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function. As an application of the method, we also do the simulation of Fisher's equation with fractional Laplacian in the monostable case.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1453
url http://hdl.handle.net/20.500.11824/1453
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/669689
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
repository.name.fl_str_mv
repository.mail.fl_str_mv
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