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An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

dc.contributor.authorHuntul, M. J.
dc.contributor.authorAbbas, Muhammad
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorID56389tr_TR
dc.date.accessioned2022-03-16T12:33:56Z
dc.date.available2022-03-16T12:33:56Z
dc.date.issued2021
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank-Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.en_US
dc.description.publishedMonth10
dc.identifier.citationHuntul, M. J.; Abbas, Muhammad; Baleanu, Dumitru (2021). "An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation", Advances in Difference Equations, Vol. 2021, No. 1.en_US
dc.identifier.doi10.1186/s13662-021-03608-1
dc.identifier.issn1687-1839
dc.identifier.issue1en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/5126
dc.identifier.volume2021en_US
dc.language.isoenen_US
dc.relation.ispartofAdvances in Difference Equationsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectHyperbolic Equationen_US
dc.subjectInverse Problemen_US
dc.subjectPeriodic Boundaryen_US
dc.subjectIntegral Boundaryen_US
dc.subjectTikhonov Regularizationen_US
dc.subjectOptimizationen_US
dc.titleAn inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equationtr_TR
dc.titleAn Inverse Problem of Reconstructing the Time-Dependent Coefficient in a One-Dimensional Hyperbolic Equationen_US
dc.typeArticleen_US
dspace.entity.typePublication

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