High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations

Detalhes bibliográficos
Autor(a) principal: Ferrás, Luís Jorge Lima
Data de Publicação: 2021
Outros Autores: Ford, Neville, Morgado, Maria Luisa, Rebelo, Magda
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/66733
Resumo: Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method.
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spelling High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equationsFractional diffusionCaputo derivativeNonpolynomial collocation methodPolynomial collocation methodMethod of linesCiências Naturais::MatemáticasScience & TechnologyTaking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method.L.L. Ferras would like to thank FCT - Fundacao para a Ciencia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) for financial support through the scholarship SFRH/BPD/100353/2014 and Project UID-MAT-00013/2013. M.L. Morgado aknowledges the financial support of FCT, through the Project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, University of Lisbon. This work was also partially supported by FCT through the Project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes).SpringerUniversidade do MinhoFerrás, Luís Jorge LimaFord, NevilleMorgado, Maria LuisaRebelo, Magda20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/66733engFerrás, L. L., Ford, N., Morgado, M. L., & Rebelo, M. (2020, January 16). High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations. Mathematics in Computer Science. Springer Science and Business Media LLC. http://doi.org/10.1007/s11786-019-00448-x1661-827010.1007/s11786-019-00448-xhttps://link.springer.com/article/10.1007%2Fs11786-019-00448-xinfo: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:RCAAP2023-07-21T12:26:46Zoai:repositorium.sdum.uminho.pt:1822/66733Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:21:14.735916Repositório 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 High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
title High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
spellingShingle High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
Ferrás, Luís Jorge Lima
Fractional diffusion
Caputo derivative
Nonpolynomial collocation method
Polynomial collocation method
Method of lines
Ciências Naturais::Matemáticas
Science & Technology
title_short High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
title_full High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
title_fullStr High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
title_full_unstemmed High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
title_sort High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
author Ferrás, Luís Jorge Lima
author_facet Ferrás, Luís Jorge Lima
Ford, Neville
Morgado, Maria Luisa
Rebelo, Magda
author_role author
author2 Ford, Neville
Morgado, Maria Luisa
Rebelo, Magda
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Ferrás, Luís Jorge Lima
Ford, Neville
Morgado, Maria Luisa
Rebelo, Magda
dc.subject.por.fl_str_mv Fractional diffusion
Caputo derivative
Nonpolynomial collocation method
Polynomial collocation method
Method of lines
Ciências Naturais::Matemáticas
Science & Technology
topic Fractional diffusion
Caputo derivative
Nonpolynomial collocation method
Polynomial collocation method
Method of lines
Ciências Naturais::Matemáticas
Science & Technology
description Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
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 https://hdl.handle.net/1822/66733
url https://hdl.handle.net/1822/66733
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Ferrás, L. L., Ford, N., Morgado, M. L., & Rebelo, M. (2020, January 16). High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations. Mathematics in Computer Science. Springer Science and Business Media LLC. http://doi.org/10.1007/s11786-019-00448-x
1661-8270
10.1007/s11786-019-00448-x
https://link.springer.com/article/10.1007%2Fs11786-019-00448-x
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 Springer
publisher.none.fl_str_mv Springer
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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