Compact schemes in time with applications to partial differential equations
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/89115 |
Resumo: | We propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demonstrate the effectiveness of the method. Then a second set of numerical benchmarks for Partial Differential Equations such as convection-diffusion, Schrodinger equation, wave equation, Burgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods. |
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Compact schemes in time with applications to partial differential equationsCompact schemeStructural equationTime discretizationVery high-orderA-stabilityDispersionCiências Naturais::MatemáticasScience & TechnologyWe propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demonstrate the effectiveness of the method. Then a second set of numerical benchmarks for Partial Differential Equations such as convection-diffusion, Schrodinger equation, wave equation, Burgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods.S. Clain and G.J. Machado acknowledge the financial support by Portuguese Funds through Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. M.T. Malheiro acknowledges the financial support by Portuguese Funds through Foundation for Science and Technology (FCT) in the framework of the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM. S. Clain, G.J. Machado, and M.T. Malheiro acknowledge the fi-nancial support by FEDER - Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 - Programa Operacional Fatores de Competitividade, POCI-01-0145-FEDER-028118 and PTDC/MAT-APL/28118/2017.ElsevierUniversidade do MinhoClain, StéphaneMachado, Gaspar J.Malheiro, M. Teresa20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/89115engClain, S., Machado, G. J., & Malheiro, M. T. (2023, June). Compact schemes in time with applications to partial differential equations. Computers & Mathematics with Applications. Elsevier BV. http://doi.org/10.1016/j.camwa.2023.03.0110898-122110.1016/j.camwa.2023.03.011https://www.sciencedirect.com/science/article/pii/S0898122123001062info: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:RCAAP2024-03-02T01:19:41Zoai:repositorium.sdum.uminho.pt:1822/89115Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:11:49.374511Repositório 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 |
Compact schemes in time with applications to partial differential equations |
title |
Compact schemes in time with applications to partial differential equations |
spellingShingle |
Compact schemes in time with applications to partial differential equations Clain, Stéphane Compact scheme Structural equation Time discretization Very high-order A-stability Dispersion Ciências Naturais::Matemáticas Science & Technology |
title_short |
Compact schemes in time with applications to partial differential equations |
title_full |
Compact schemes in time with applications to partial differential equations |
title_fullStr |
Compact schemes in time with applications to partial differential equations |
title_full_unstemmed |
Compact schemes in time with applications to partial differential equations |
title_sort |
Compact schemes in time with applications to partial differential equations |
author |
Clain, Stéphane |
author_facet |
Clain, Stéphane Machado, Gaspar J. Malheiro, M. Teresa |
author_role |
author |
author2 |
Machado, Gaspar J. Malheiro, M. Teresa |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Clain, Stéphane Machado, Gaspar J. Malheiro, M. Teresa |
dc.subject.por.fl_str_mv |
Compact scheme Structural equation Time discretization Very high-order A-stability Dispersion Ciências Naturais::Matemáticas Science & Technology |
topic |
Compact scheme Structural equation Time discretization Very high-order A-stability Dispersion Ciências Naturais::Matemáticas Science & Technology |
description |
We propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demonstrate the effectiveness of the method. Then a second set of numerical benchmarks for Partial Differential Equations such as convection-diffusion, Schrodinger equation, wave equation, Burgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023 2023-01-01T00:00:00Z |
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/1822/89115 |
url |
https://hdl.handle.net/1822/89115 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Clain, S., Machado, G. J., & Malheiro, M. T. (2023, June). Compact schemes in time with applications to partial differential equations. Computers & Mathematics with Applications. Elsevier BV. http://doi.org/10.1016/j.camwa.2023.03.011 0898-1221 10.1016/j.camwa.2023.03.011 https://www.sciencedirect.com/science/article/pii/S0898122123001062 |
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 |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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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1799137768475983872 |