Absolutely stable difference scheme for a general class of singular perturbation problems

Detalhes bibliográficos
Autor(a) principal: El-Zahar, Essam R.
Data de Publicação: 2020
Outros Autores: Alotaibi, A. M., Ebaid, Abdelhalim, Baleanu, Dumitru, Machado, J. A. Tenreiro, Hamed, Y. S.
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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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
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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
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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)
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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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