An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation
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 inves...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03608-1 |
| _version_ | 1831657574891520000 |
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| author | M. J. Huntul Muhammad Abbas Dumitru Baleanu |
| author_facet | M. J. Huntul Muhammad Abbas Dumitru Baleanu |
| author_sort | M. J. Huntul |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T17:29:30Z |
| format | Article |
| id | doaj.art-bcc4cfbd0da4415aac53e9949c1260a7 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T17:29:30Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-bcc4cfbd0da4415aac53e9949c1260a72022-12-21T20:12:29ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021111710.1186/s13662-021-03608-1An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equationM. J. Huntul0Muhammad Abbas1Dumitru Baleanu2Department of Mathematics, Faculty of Science, Jazan UniversityDepartment of Mathematics, University of SargodhaDepartment of Mathematics, Faculty of Arts and Sciences, Çankaya UniversityAbstract 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.https://doi.org/10.1186/s13662-021-03608-1Hyperbolic equationInverse problemPeriodic boundaryIntegral boundaryTikhonov regularizationOptimization |
| spellingShingle | M. J. Huntul Muhammad Abbas Dumitru Baleanu An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation Advances in Difference Equations Hyperbolic equation Inverse problem Periodic boundary Integral boundary Tikhonov regularization Optimization |
| title | An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation |
| title_full | An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation |
| title_fullStr | An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation |
| title_full_unstemmed | An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation |
| title_short | An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation |
| title_sort | inverse problem of reconstructing the time dependent coefficient in a one dimensional hyperbolic equation |
| topic | Hyperbolic equation Inverse problem Periodic boundary Integral boundary Tikhonov regularization Optimization |
| url | https://doi.org/10.1186/s13662-021-03608-1 |
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