Spherical Spline Solutions of an Inhomogeneous Biharmonic Equation Full article
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Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2024, Volume: 64, Number: 8, Pages: 1765-1774 Pages count : 10 DOI: 10.1134/s0965542524700817 | ||||
| Tags | biharmonic equation, spherical Sobolev spaces, extremal functions, splines | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0008 |
Abstract:
An inhomogeneous biharmonic equation is considered on a unit sphere of three-dimensional space. The solution of this equation belonging to the spherical Sobolev space is approximated by a sequence of solutions of the same equation, but with special right-hand sides, which are linear combinations of shifts of the Dirac delta function. It is proved that, for given nodes on the sphere that determine shifts, there exist special solutions of the equation: spherical biharmonic splines, and the weights corresponding to each of them are solutions of the accompanying nondegenerate system of linear algebraic equations. A relation is established between the quality of approximation of the solution of the differential problem by spherical biharmonic splines and the problem of the convergence rate of optimal weighted spherical cubature formulas.
Cite:
Vaskevich V.L.
Spherical Spline Solutions of an Inhomogeneous Biharmonic Equation
Computational Mathematics and Mathematical Physics. 2024. V.64. N8. P.1765-1774. DOI: 10.1134/s0965542524700817 WOS Scopus РИНЦ OpenAlex
Spherical Spline Solutions of an Inhomogeneous Biharmonic Equation
Computational Mathematics and Mathematical Physics. 2024. V.64. N8. P.1765-1774. DOI: 10.1134/s0965542524700817 WOS Scopus РИНЦ OpenAlex
Original:
Васкевич В.Л.
Сферические сплайн-решения неоднородного бигармонического уравнения
Журнал вычислительной математики и математической физики. 2024. Т.64. №8. С.1454–1463. DOI: 10.31857/S0044466924080107 РИНЦ OpenAlex
Сферические сплайн-решения неоднородного бигармонического уравнения
Журнал вычислительной математики и математической физики. 2024. Т.64. №8. С.1454–1463. DOI: 10.31857/S0044466924080107 РИНЦ OpenAlex
Dates:
| Submitted: | Mar 5, 2024 |
| Accepted: | May 5, 2024 |
| Published print: | Sep 26, 2024 |
| Published online: | Sep 26, 2024 |
Identifiers:
| Web of science: | WOS:001324967400005 |
| Scopus: | 2-s2.0-85205289609 |
| Elibrary: | 69921025 |
| OpenAlex: | W4402883606 |
Citing:
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