Inverse problems for discrete Hermite nabla difference equation
Inverse problems are studied for discrete Hermite equations with nabla difference including initial value, terminal value and Sturm–Liouville problems. A quantitative study is conducted to obtain the solution. The problem with initial value and terminal value conditions is transformed into a simple...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2431000 |
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| author | B. Shiri Y. Guang D. Baleanu |
| author_facet | B. Shiri Y. Guang D. Baleanu |
| author_sort | B. Shiri |
| collection | DOAJ |
| description | Inverse problems are studied for discrete Hermite equations with nabla difference including initial value, terminal value and Sturm–Liouville problems. A quantitative study is conducted to obtain the solution. The problem with initial value and terminal value conditions is transformed into a simple recursive formula while the Sturm–Liouville problem is transformed into a generalized eigenvalue problem. Some analyses related to the corresponding matrix are done. The eigenvalues are computed using the determinant of the corresponding pencil matrix. Furthermore, a simple and fast recursive algorithm is proposed for computing corresponding eigenvectors. Several examples are provided to explain the method simply and to demonstrate the numerical results. |
| format | Article |
| id | doaj-art-cd2d7aa59cb34547ade1dbcbe635cb57 |
| institution | DOAJ |
| issn | 2769-0911 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-cd2d7aa59cb34547ade1dbcbe635cb572025-08-20T02:49:16ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112025-12-0133110.1080/27690911.2024.2431000Inverse problems for discrete Hermite nabla difference equationB. Shiri0Y. Guang1D. Baleanu2Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, People's Republic of ChinaSchool of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, People's Republic of ChinaDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonInverse problems are studied for discrete Hermite equations with nabla difference including initial value, terminal value and Sturm–Liouville problems. A quantitative study is conducted to obtain the solution. The problem with initial value and terminal value conditions is transformed into a simple recursive formula while the Sturm–Liouville problem is transformed into a generalized eigenvalue problem. Some analyses related to the corresponding matrix are done. The eigenvalues are computed using the determinant of the corresponding pencil matrix. Furthermore, a simple and fast recursive algorithm is proposed for computing corresponding eigenvectors. Several examples are provided to explain the method simply and to demonstrate the numerical results.https://www.tandfonline.com/doi/10.1080/27690911.2024.2431000Sturm–Liouville problemsdiscrete Hermite equationsSchrödinger equationgeneralized eigenvalue problemquantum harmonic oscillator41A27 |
| spellingShingle | B. Shiri Y. Guang D. Baleanu Inverse problems for discrete Hermite nabla difference equation Applied Mathematics in Science and Engineering Sturm–Liouville problems discrete Hermite equations Schrödinger equation generalized eigenvalue problem quantum harmonic oscillator 41A27 |
| title | Inverse problems for discrete Hermite nabla difference equation |
| title_full | Inverse problems for discrete Hermite nabla difference equation |
| title_fullStr | Inverse problems for discrete Hermite nabla difference equation |
| title_full_unstemmed | Inverse problems for discrete Hermite nabla difference equation |
| title_short | Inverse problems for discrete Hermite nabla difference equation |
| title_sort | inverse problems for discrete hermite nabla difference equation |
| topic | Sturm–Liouville problems discrete Hermite equations Schrödinger equation generalized eigenvalue problem quantum harmonic oscillator 41A27 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2431000 |
| work_keys_str_mv | AT bshiri inverseproblemsfordiscretehermitenabladifferenceequation AT yguang inverseproblemsfordiscretehermitenabladifferenceequation AT dbaleanu inverseproblemsfordiscretehermitenabladifferenceequation |