Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions
This study aims to find the time-dependent potential terms in the two inverse problems of the third-order pseudo-parabolic with initial and various boundary conditions supplemented by the overdetermination data. The nonlinear inverse problems have significant applications in physics and engineering...
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| Format: | Article |
| Language: | English |
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University of Baghdad
2025-01-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
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| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3671 |
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| author | Mohammed S. Hussein Sayl Gani Taysir E. Dyhoum |
| author_facet | Mohammed S. Hussein Sayl Gani Taysir E. Dyhoum |
| author_sort | Mohammed S. Hussein |
| collection | DOAJ |
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This study aims to find the time-dependent potential terms in the two inverse problems of the third-order pseudo-parabolic with initial and various boundary conditions supplemented by the overdetermination data. The nonlinear inverse problems have significant applications in physics and engineering fields. We proved the existence and uniqueness of the solution of the two problems are being proved, but they still need to be proposed (since tiny perturbations in input data cause considerable errors in the output potential term). Consequently, the regularized methods should be employed. A finite difference schema is used for solving direct problems. In contrast, the inverse problems were reformulated as nonlinear least-square minimization and solved efficiently by optimizing MATLAB routine lsqnonlin. Tikhonov's regularization method was applied to get stable results. The numerical results were explained by presenting a test example for each problem. In addition, the stability was discussed by utilizing the Von Neumann stability analysis. The results showed that the time-dependent potential terms were reconstructed successfully and were stable and accurate.
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| format | Article |
| id | doaj-art-0a81359f4dcf4c6494cad06e355eaafe |
| institution | Kabale University |
| issn | 1609-4042 2521-3407 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj-art-0a81359f4dcf4c6494cad06e355eaafe2025-01-22T01:21:04ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072025-01-0138110.30526/38.1.3671Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra ConditionsMohammed S. Hussein0https://orcid.org/0000-0002-9456-4303Sayl Gani1https://orcid.org/0000-0003-4595-2251Taysir E. Dyhoum2https://orcid.org/0000-0002-1761-5904Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.Department of Computer Techniques Engineering, Imam Al-Kadhum College, Baghdad, IraqDepartment of Computing and Mathematics, Faculty of Science and Engineering, Manchester Metropolitan University, Manchester, UK This study aims to find the time-dependent potential terms in the two inverse problems of the third-order pseudo-parabolic with initial and various boundary conditions supplemented by the overdetermination data. The nonlinear inverse problems have significant applications in physics and engineering fields. We proved the existence and uniqueness of the solution of the two problems are being proved, but they still need to be proposed (since tiny perturbations in input data cause considerable errors in the output potential term). Consequently, the regularized methods should be employed. A finite difference schema is used for solving direct problems. In contrast, the inverse problems were reformulated as nonlinear least-square minimization and solved efficiently by optimizing MATLAB routine lsqnonlin. Tikhonov's regularization method was applied to get stable results. The numerical results were explained by presenting a test example for each problem. In addition, the stability was discussed by utilizing the Von Neumann stability analysis. The results showed that the time-dependent potential terms were reconstructed successfully and were stable and accurate. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3671Pseudoparabolic inverse problemTikhonov regularization methodFinite difference methodVon Neumann stability analysis |
| spellingShingle | Mohammed S. Hussein Sayl Gani Taysir E. Dyhoum Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions Ibn Al-Haitham Journal for Pure and Applied Sciences Pseudoparabolic inverse problem Tikhonov regularization method Finite difference method Von Neumann stability analysis |
| title | Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions |
| title_full | Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions |
| title_fullStr | Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions |
| title_full_unstemmed | Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions |
| title_short | Timewise–dependent Coefficients Identification Problems for Third-Order Pseudo-Parabolic Equations from Nonlocal Extra Conditions |
| title_sort | timewise dependent coefficients identification problems for third order pseudo parabolic equations from nonlocal extra conditions |
| topic | Pseudoparabolic inverse problem Tikhonov regularization method Finite difference method Von Neumann stability analysis |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3671 |
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