Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation

Detalhes bibliográficos
Autor(a) principal: Bhrawy, Ali H.
Data de Publicação: 2016
Outros Autores: Zaky, Mahmoud A., Machado, J. A. Tenreiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/9406
Resumo: The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shiftedChebyshev polynomials, are presented and derived.We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractionalorder telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices.We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.
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spelling Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau ApproximationFractional telegraph equationFractional Klein–Gordon equationOperational matrixShifted Chebyshev Tau methodRiesz fractional derivativeThe operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shiftedChebyshev polynomials, are presented and derived.We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractionalorder telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices.We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.Springer VerlagRepositório Científico do Instituto Politécnico do PortoBhrawy, Ali H.Zaky, Mahmoud A.Machado, J. A. Tenreiro20162117-01-01T00:00:00Z2016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/9406eng10.1007/s10957-016-0863-8metadata 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:RCAAP2023-03-13T12:50:47Zoai:recipp.ipp.pt:10400.22/9406Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:30:00.689238Repositório 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 Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
title Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
spellingShingle Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
Bhrawy, Ali H.
Fractional telegraph equation
Fractional Klein–Gordon equation
Operational matrix
Shifted Chebyshev Tau method
Riesz fractional derivative
title_short Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
title_full Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
title_fullStr Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
title_full_unstemmed Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
title_sort Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
author Bhrawy, Ali H.
author_facet Bhrawy, Ali H.
Zaky, Mahmoud A.
Machado, J. A. Tenreiro
author_role author
author2 Zaky, Mahmoud A.
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 Bhrawy, Ali H.
Zaky, Mahmoud A.
Machado, J. A. Tenreiro
dc.subject.por.fl_str_mv Fractional telegraph equation
Fractional Klein–Gordon equation
Operational matrix
Shifted Chebyshev Tau method
Riesz fractional derivative
topic Fractional telegraph equation
Fractional Klein–Gordon equation
Operational matrix
Shifted Chebyshev Tau method
Riesz fractional derivative
description The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shiftedChebyshev polynomials, are presented and derived.We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractionalorder telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices.We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.
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
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.22/9406
url http://hdl.handle.net/10400.22/9406
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1007/s10957-016-0863-8
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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
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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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