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

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dc.contributor.author Huntul, M. J.
dc.contributor.author Abbas, Muhammad
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2022-03-16T12:33:56Z
dc.date.available 2022-03-16T12:33:56Z
dc.date.issued 2021-10-15
dc.identifier.citation Huntul, 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. tr_TR
dc.identifier.issn 1687-1839
dc.identifier.uri http://hdl.handle.net/20.500.12416/5126
dc.description.abstract In 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. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1186/s13662-021-03608-1 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Hyperbolic Equation tr_TR
dc.subject Inverse Problem tr_TR
dc.subject Periodic Boundary tr_TR
dc.subject Integral Boundary tr_TR
dc.subject Tikhonov Regularization tr_TR
dc.subject Optimization tr_TR
dc.title An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation tr_TR
dc.type article tr_TR
dc.relation.journal Advances in Difference Equations tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 2021 tr_TR
dc.identifier.issue 1 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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