Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10400.22/18646 |
Resumo: | This paper presents a meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD). The algorithm is used for finding the approximate solution of nonlinear anomalous reaction–diffusion models. The time discretization procedure is carried out by means of a weighted discrete scheme covering second-order approximation, while the spatial discretization is accomplished using the RBF-FD. The theoretical discussion validates the stability and convergence of the time-discretized formulation which are analyzed in the perspective to the H1-norm. This approach benefits from a local collocation technique to estimate the differential operators using the weighted differences over local collection nodes through the RBF expansion. Two test problems illustrate the computational efficiency of the approach. Numerical simulations highlight the performance of the method that provides accurate solutions on complex domains with any distribution node type. |
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Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistryNonlinear anomalous reaction–diffusion processRiemann–Liouville fractional derivativeRBF-FDError analysisThis paper presents a meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD). The algorithm is used for finding the approximate solution of nonlinear anomalous reaction–diffusion models. The time discretization procedure is carried out by means of a weighted discrete scheme covering second-order approximation, while the spatial discretization is accomplished using the RBF-FD. The theoretical discussion validates the stability and convergence of the time-discretized formulation which are analyzed in the perspective to the H1-norm. This approach benefits from a local collocation technique to estimate the differential operators using the weighted differences over local collection nodes through the RBF expansion. Two test problems illustrate the computational efficiency of the approach. Numerical simulations highlight the performance of the method that provides accurate solutions on complex domains with any distribution node type.The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions.ElsevierRepositório Científico do Instituto Politécnico do PortoNikan, O.Avazzadeh, Z.Machado, J. A. Tenreiro20212031-12-01T00:00:00Z2021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/18646eng10.1016/j.jocs.2021.101394info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T13:10:48Zoai:recipp.ipp.pt:10400.22/18646Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:38:11.991955Repositório 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 study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
title |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
spellingShingle |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry Nikan, O. Nonlinear anomalous reaction–diffusion process Riemann–Liouville fractional derivative RBF-FD Error analysis |
title_short |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
title_full |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
title_fullStr |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
title_full_unstemmed |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
title_sort |
Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry |
author |
Nikan, O. |
author_facet |
Nikan, O. Avazzadeh, Z. Machado, J. A. Tenreiro |
author_role |
author |
author2 |
Avazzadeh, Z. Machado, J. A. Tenreiro |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Nikan, O. Avazzadeh, Z. Machado, J. A. Tenreiro |
dc.subject.por.fl_str_mv |
Nonlinear anomalous reaction–diffusion process Riemann–Liouville fractional derivative RBF-FD Error analysis |
topic |
Nonlinear anomalous reaction–diffusion process Riemann–Liouville fractional derivative RBF-FD Error analysis |
description |
This paper presents a meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD). The algorithm is used for finding the approximate solution of nonlinear anomalous reaction–diffusion models. The time discretization procedure is carried out by means of a weighted discrete scheme covering second-order approximation, while the spatial discretization is accomplished using the RBF-FD. The theoretical discussion validates the stability and convergence of the time-discretized formulation which are analyzed in the perspective to the H1-norm. This approach benefits from a local collocation technique to estimate the differential operators using the weighted differences over local collection nodes through the RBF expansion. Two test problems illustrate the computational efficiency of the approach. Numerical simulations highlight the performance of the method that provides accurate solutions on complex domains with any distribution node type. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 2021-01-01T00:00:00Z 2031-12-01T00:00:00Z |
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 |
http://hdl.handle.net/10400.22/18646 |
url |
http://hdl.handle.net/10400.22/18646 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1016/j.jocs.2021.101394 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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) |
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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1799131471790735360 |