Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908824303042560 |
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| author | Shadimetov, Kh. M. Karimov, R. S. |
| author_facet | Shadimetov, Kh. M. Karimov, R. S. |
| contents | This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$. Here, representations of optimal coefficients of explicit finite-difference formulas of the Adams type on classes $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$ for any $m\ge 3$ will be found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space Shadimetov, Kh. M. Karimov, R. S. Numerical Analysis This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$. Here, representations of optimal coefficients of explicit finite-difference formulas of the Adams type on classes $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$ for any $m\ge 3$ will be found. |
| title | Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.06643 |