Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics
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/10400.22/19004 |
Resumo: | This paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via a finite difference algorithm, while the spatial discretization is obtained using the local radial basis function in a finite difference mode. The local collocation method approximates the differential operators using a weighted sum of the function values over a local collection of nodes (named stencil) through a radial basis function expansion. This technique considers merely the discretization nodes of each subdomain around the collocation node. This leads to sparse systems and tackles the ill-conditioning produced of global collocation. The theoretical convergence and stability analyses of the proposed time semi-discrete scheme are proved by means of the discrete energy method. Numerical results confirm the accuracy and efficiency of the new approach. |
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Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamicsCaputo fractional derivativeTime fractional Tricomi-type modelLRBF-FDStability analysisThis paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via a finite difference algorithm, while the spatial discretization is obtained using the local radial basis function in a finite difference mode. The local collocation method approximates the differential operators using a weighted sum of the function values over a local collection of nodes (named stencil) through a radial basis function expansion. This technique considers merely the discretization nodes of each subdomain around the collocation node. This leads to sparse systems and tackles the ill-conditioning produced of global collocation. The theoretical convergence and stability analyses of the proposed time semi-discrete scheme are proved by means of the discrete energy method. Numerical results confirm the accuracy and efficiency of the new approach.The authors are very grateful to the reviewers for their valuable comments on the manuscript that led to many improvements.ElsevierRepositório Científico do Instituto Politécnico do PortoNikan, O.Machado, J. A. TenreiroAvazzadeh, Z.Jafari, H.2021-12-07T10:49:31Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/19004eng2090-123210.1016/j.jare.2020.06.018info: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:RCAAP2023-03-13T13:12:46Zoai:recipp.ipp.pt:10400.22/19004Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:39:04.333816Repositório 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 evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
title |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
spellingShingle |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics Nikan, O. Caputo fractional derivative Time fractional Tricomi-type model LRBF-FD Stability analysis |
title_short |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
title_full |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
title_fullStr |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
title_full_unstemmed |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
title_sort |
Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics |
author |
Nikan, O. |
author_facet |
Nikan, O. Machado, J. A. Tenreiro Avazzadeh, Z. Jafari, H. |
author_role |
author |
author2 |
Machado, J. A. Tenreiro Avazzadeh, Z. Jafari, H. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Nikan, O. Machado, J. A. Tenreiro Avazzadeh, Z. Jafari, H. |
dc.subject.por.fl_str_mv |
Caputo fractional derivative Time fractional Tricomi-type model LRBF-FD Stability analysis |
topic |
Caputo fractional derivative Time fractional Tricomi-type model LRBF-FD Stability analysis |
description |
This paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via a finite difference algorithm, while the spatial discretization is obtained using the local radial basis function in a finite difference mode. The local collocation method approximates the differential operators using a weighted sum of the function values over a local collection of nodes (named stencil) through a radial basis function expansion. This technique considers merely the discretization nodes of each subdomain around the collocation node. This leads to sparse systems and tackles the ill-conditioning produced of global collocation. The theoretical convergence and stability analyses of the proposed time semi-discrete scheme are proved by means of the discrete energy method. Numerical results confirm the accuracy and efficiency of the new approach. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 2020-01-01T00:00:00Z 2021-12-07T10:49:31Z |
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/10400.22/19004 |
url |
http://hdl.handle.net/10400.22/19004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2090-1232 10.1016/j.jare.2020.06.018 |
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 |
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) |
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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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1799131479037444096 |