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On the convergence of a numerical method for a hypersingular integral equation on a closed surfaceстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 2 ноября 2015 г.
- Авторы: Ryzhakov G.V., Setukha A.V.
- Журнал: Differential Equations
- Том: 46
- Номер: 9
- Год издания: 2010
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1353
- Последняя страница: 1363
- DOI: 10.1134/S0012266110090119
- Аннотация: We consider a linear integral equation with a hypersingular integral treated in the sense of the Hadamard finite value. This equation arises in the solution of the Neumann boundary value problem for the Laplace equation with a representation of a solution in the form of a double-layer potential. We consider the case in which the interior or exterior boundary value problem is solved in a domain; whose boundary is a smooth closed surface, and an integral equation is written out on that surface. For the integral operator in that equation, we suggest quadrature formulas like the method of vortical frames with a regularization, which provides its approximation on the entire surface for the use of a nonstructured partition. We construct a numerical scheme for the integral equation on the basis of suggested quadrature formulas, prove an estimate for the norm of the inverse matrix of the related system of linear equations and the uniform convergence of numerical solutions to the exact solution of the hypersingular integral equation on the grid.
- Добавил в систему: Сетуха Алексей Викторович