Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10316/37168 https://doi.org/10.1016/j.cnsns.2017.03.004 |
Resumo: | We present a numerical method to solve a time-space fractional Fokker-Planck equation with a spacetime dependent force field F(x, t), and diffusion d(x, t). When the problem being modelled includes time dependent coefficients, the time fractional operator, that typically appears on the right hand side of the fractional equation, should not act on those coefficients and consequently the differential equation can not be simplified using the standard technique of transferring the time fractional operator to the left hand side of the equation. We take this into account when deriving the numerical method. Discussions on the unconditional stability and accuracy of the method are presented, including results that show the order of convergence is affected by the regularity of solutions. The numerical experiments confirm that the convergence of the method is second order in time and space for sufficiently regular solutions and they also illustrate how the order of convergence can depend on the regularity of the solutions. In this case, the rate of convergence can be improved by considering a non-uniform mesh. |
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Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusionFokker-Planck equationTime-dependent force field and diffusionFractional derivativesFinite differencesFourier analysisWe present a numerical method to solve a time-space fractional Fokker-Planck equation with a spacetime dependent force field F(x, t), and diffusion d(x, t). When the problem being modelled includes time dependent coefficients, the time fractional operator, that typically appears on the right hand side of the fractional equation, should not act on those coefficients and consequently the differential equation can not be simplified using the standard technique of transferring the time fractional operator to the left hand side of the equation. We take this into account when deriving the numerical method. Discussions on the unconditional stability and accuracy of the method are presented, including results that show the order of convergence is affected by the regularity of solutions. The numerical experiments confirm that the convergence of the method is second order in time and space for sufficiently regular solutions and they also illustrate how the order of convergence can depend on the regularity of the solutions. In this case, the rate of convergence can be improved by considering a non-uniform mesh.Elsevier2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/37168http://hdl.handle.net/10316/37168https://doi.org/10.1016/j.cnsns.2017.03.004https://doi.org/10.1016/j.cnsns.2017.03.004eng1007-5704http://www.sciencedirect.com/science/article/pii/S1007570417300813Pinto, LuísSousa, Ercíliainfo: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:RCAAP2021-06-29T10:02:58Zoai:estudogeral.uc.pt:10316/37168Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:39.617348Repositório 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 |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
title |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
spellingShingle |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion Pinto, Luís Fokker-Planck equation Time-dependent force field and diffusion Fractional derivatives Finite differences Fourier analysis |
title_short |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
title_full |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
title_fullStr |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
title_full_unstemmed |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
title_sort |
Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion |
author |
Pinto, Luís |
author_facet |
Pinto, Luís Sousa, Ercília |
author_role |
author |
author2 |
Sousa, Ercília |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Pinto, Luís Sousa, Ercília |
dc.subject.por.fl_str_mv |
Fokker-Planck equation Time-dependent force field and diffusion Fractional derivatives Finite differences Fourier analysis |
topic |
Fokker-Planck equation Time-dependent force field and diffusion Fractional derivatives Finite differences Fourier analysis |
description |
We present a numerical method to solve a time-space fractional Fokker-Planck equation with a spacetime dependent force field F(x, t), and diffusion d(x, t). When the problem being modelled includes time dependent coefficients, the time fractional operator, that typically appears on the right hand side of the fractional equation, should not act on those coefficients and consequently the differential equation can not be simplified using the standard technique of transferring the time fractional operator to the left hand side of the equation. We take this into account when deriving the numerical method. Discussions on the unconditional stability and accuracy of the method are presented, including results that show the order of convergence is affected by the regularity of solutions. The numerical experiments confirm that the convergence of the method is second order in time and space for sufficiently regular solutions and they also illustrate how the order of convergence can depend on the regularity of the solutions. In this case, the rate of convergence can be improved by considering a non-uniform mesh. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 |
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/10316/37168 http://hdl.handle.net/10316/37168 https://doi.org/10.1016/j.cnsns.2017.03.004 https://doi.org/10.1016/j.cnsns.2017.03.004 |
url |
http://hdl.handle.net/10316/37168 https://doi.org/10.1016/j.cnsns.2017.03.004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1007-5704 http://www.sciencedirect.com/science/article/pii/S1007570417300813 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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 |
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1799133897085157377 |