Реферат: 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.

Библиографическая ссылка: 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

Оригинальная: 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

Даты:

Поступила в редакцию:	5 мар. 2024 г.
Принята к публикации:	5 мая 2024 г.
Опубликована в печати:	26 сент. 2024 г.
Опубликована online:	26 сент. 2024 г.

Идентификаторы БД:

Web of science:	WOS:001324967400005
Scopus:	2-s2.0-85205289609
РИНЦ:	69921025
OpenAlex:	W4402883606

Цитирование в БД: Пока нет цитирований

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