Absolutely stable difference scheme for a general class of singular perturbation problems
Autor(a) principal: | |
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Data de Publicação: | 2020 |
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/10400.22/18546 |
Resumo: | This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
Absolutely stable difference scheme for a general class of singular perturbation problemsSingular perturbation problemsFinite difference schemesAbsolutely stableBoundary and interior layersThis paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.SpringerRepositório Científico do Instituto Politécnico do PortoEl-Zahar, Essam R.Alotaibi, A. M.Ebaid, AbdelhalimBaleanu, DumitruMachado, J. A. TenreiroHamed, Y. S.2021-09-24T14:52:42Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/18546eng10.1186/s13662-020-02862-zinfo: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:RCAAP2023-03-13T13:10:15Zoai:recipp.ipp.pt:10400.22/18546Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:38:04.214881Repositório 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 |
Absolutely stable difference scheme for a general class of singular perturbation problems |
title |
Absolutely stable difference scheme for a general class of singular perturbation problems |
spellingShingle |
Absolutely stable difference scheme for a general class of singular perturbation problems El-Zahar, Essam R. Singular perturbation problems Finite difference schemes Absolutely stable Boundary and interior layers |
title_short |
Absolutely stable difference scheme for a general class of singular perturbation problems |
title_full |
Absolutely stable difference scheme for a general class of singular perturbation problems |
title_fullStr |
Absolutely stable difference scheme for a general class of singular perturbation problems |
title_full_unstemmed |
Absolutely stable difference scheme for a general class of singular perturbation problems |
title_sort |
Absolutely stable difference scheme for a general class of singular perturbation problems |
author |
El-Zahar, Essam R. |
author_facet |
El-Zahar, Essam R. Alotaibi, A. M. Ebaid, Abdelhalim Baleanu, Dumitru Machado, J. A. Tenreiro Hamed, Y. S. |
author_role |
author |
author2 |
Alotaibi, A. M. Ebaid, Abdelhalim Baleanu, Dumitru Machado, J. A. Tenreiro Hamed, Y. S. |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
El-Zahar, Essam R. Alotaibi, A. M. Ebaid, Abdelhalim Baleanu, Dumitru Machado, J. A. Tenreiro Hamed, Y. S. |
dc.subject.por.fl_str_mv |
Singular perturbation problems Finite difference schemes Absolutely stable Boundary and interior layers |
topic |
Singular perturbation problems Finite difference schemes Absolutely stable Boundary and interior layers |
description |
This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 2020-01-01T00:00:00Z 2021-09-24T14:52:42Z |
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/10400.22/18546 |
url |
http://hdl.handle.net/10400.22/18546 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1186/s13662-020-02862-z |
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 |
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1799131470109868032 |