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

2016Journal article Restricted access
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dc.contributor.authorBhrawy, Ali H.
dc.contributor.authorZaky, Mahmoud A.
dc.contributor.authorMachado, J. A. Tenreiro
dc.date.accessioned2017-01-25T15:24:51Z
dc.date.embargo2117
dc.date.issued2016
dc.description.abstractThe 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1007/s10957-016-0863-8pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.22/9406
dc.language.isoengpt_PT
dc.publisherSpringer Verlagpt_PT
dc.relation.ispartofseriesJournal of Optimization Theory and Applications;
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s10957-016-0863-8pt_PT
dc.subjectFractional telegraph equationpt_PT
dc.subjectFractional Klein–Gordon equationpt_PT
dc.subjectOperational matrixpt_PT
dc.subjectShifted Chebyshev Tau methodpt_PT
dc.subjectRiesz fractional derivativept_PT
dc.titleNumerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximationpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.titleJournal of Optimization Theory and Applicationspt_PT
person.familyNameTenreiro Machado
person.givenNameJ. A.
person.identifier.ciencia-id7A18-4935-5B29
person.identifier.orcid0000-0003-4274-4879
person.identifier.ridM-2173-2013
person.identifier.scopus-author-id55989030100
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication82cd5c17-07b6-492b-b3e3-ecebdad1254f
relation.isAuthorOfPublication.latestForDiscovery82cd5c17-07b6-492b-b3e3-ecebdad1254f

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