An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations

Detalhes bibliográficos
Autor(a) principal: Zaky, M. A.
Data de Publicação: 2016
Outros Autores: Ezz-Eldien, S. S., Doha, E. H., Machado, J. A. Tenreiro, Bhrawy, A. H.
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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spelling 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
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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
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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)
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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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