Recovery of the rod cross section shape
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912235813601280 |
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| author | Kravchenko, Vladislav V. Torba, Sergii M. Vatulyan, Alexander O. |
| author_facet | Kravchenko, Vladislav V. Torba, Sergii M. Vatulyan, Alexander O. |
| contents | A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The first coefficient of the representation is sufficient for the recovery of the unknown function. A system of linear algebraic equations for finding this coefficient is obtained. The proposed method leads to an efficient numerical algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recovery of the rod cross section shape Kravchenko, Vladislav V. Torba, Sergii M. Vatulyan, Alexander O. Numerical Analysis Mathematical Physics Classical Analysis and ODEs 34A55, 34B05, 34B24, 34B60, 34L40, 35L05, 35R30, 65L09, 65N21 A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The first coefficient of the representation is sufficient for the recovery of the unknown function. A system of linear algebraic equations for finding this coefficient is obtained. The proposed method leads to an efficient numerical algorithm. |
| title | Recovery of the rod cross section shape |
| topic | Numerical Analysis Mathematical Physics Classical Analysis and ODEs 34A55, 34B05, 34B24, 34B60, 34L40, 35L05, 35R30, 65L09, 65N21 |
| url | https://arxiv.org/abs/2502.12368 |