Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917095828094976 |
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| author | Altybay, Arshyn Tokmagambetov, Niyaz Nalzhupbayeva, Gulzat |
| author_facet | Altybay, Arshyn Tokmagambetov, Niyaz Nalzhupbayeva, Gulzat |
| contents | We address the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a fractional Laplacian subject to Dirichlet boundary conditions and an integral nonlocal data. An a priori estimate is established to ensure the uniqueness and stability of the solution. A fully implicit Crank-Nicolson (CN) finite-difference scheme is proposed and rigorously analysed for stability and convergence. An efficient noise-stable computation algorithm is developed and verified through numerical experiments, demonstrating accuracy and robustness under noisy data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian Altybay, Arshyn Tokmagambetov, Niyaz Nalzhupbayeva, Gulzat Numerical Analysis Mathematical Physics 65M06, 65M32, 35R30, 35B45 We address the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a fractional Laplacian subject to Dirichlet boundary conditions and an integral nonlocal data. An a priori estimate is established to ensure the uniqueness and stability of the solution. A fully implicit Crank-Nicolson (CN) finite-difference scheme is proposed and rigorously analysed for stability and convergence. An efficient noise-stable computation algorithm is developed and verified through numerical experiments, demonstrating accuracy and robustness under noisy data. |
| title | Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian |
| topic | Numerical Analysis Mathematical Physics 65M06, 65M32, 35R30, 35B45 |
| url | https://arxiv.org/abs/2511.16238 |