An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10400.22/9414 |
Resumo: | This paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1þ1 and 2þ1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion EquationsOperational matrixCollocation methodVariable-order anomalous diffusionChebyshev polynomialsThis paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1þ1 and 2þ1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones.American Society of Mechanical EngineersRepositório Científico do Instituto Politécnico do PortoZaky, M. A.Ezz-Eldien, S. S.Doha, E. H.Machado, J. A. TenreiroBhrawy, A. H.20162117-01-01T00:00:00Z2016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/9414eng10.1115/1.4033723metadata only accessinfo: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:RCAAP2023-03-13T12:50:48Zoai:recipp.ipp.pt:10400.22/9414Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:30:01.035641Repositório 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 |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
title |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
spellingShingle |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations Zaky, M. A. Operational matrix Collocation method Variable-order anomalous diffusion Chebyshev polynomials |
title_short |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
title_full |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
title_fullStr |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
title_full_unstemmed |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
title_sort |
An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations |
author |
Zaky, M. A. |
author_facet |
Zaky, M. A. Ezz-Eldien, S. S. Doha, E. H. Machado, J. A. Tenreiro Bhrawy, A. H. |
author_role |
author |
author2 |
Ezz-Eldien, S. S. Doha, E. H. Machado, J. A. Tenreiro Bhrawy, A. H. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Zaky, M. A. Ezz-Eldien, S. S. Doha, E. H. Machado, J. A. Tenreiro Bhrawy, A. H. |
dc.subject.por.fl_str_mv |
Operational matrix Collocation method Variable-order anomalous diffusion Chebyshev polynomials |
topic |
Operational matrix Collocation method Variable-order anomalous diffusion Chebyshev polynomials |
description |
This paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1þ1 and 2þ1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 2016-01-01T00:00:00Z 2117-01-01T00:00:00Z |
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 |
http://hdl.handle.net/10400.22/9414 |
url |
http://hdl.handle.net/10400.22/9414 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1115/1.4033723 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
American Society of Mechanical Engineers |
publisher.none.fl_str_mv |
American Society of Mechanical Engineers |
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) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131395874881536 |