|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ФИЦ ПХФ и МХ РАН |
||
Convergence of the Method of Piecewise Linear Approximations and Collocations for a Two-Dimensional Hypersingular Integral Equation on a Set with Boundaryстатья
- Автор: Setukha A.V.
- Журнал: Differential Equations
- Том: 60
- Номер: 9
- Год издания: 2024
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1284
- Последняя страница: 1304
- DOI: 10.1134/S001226612409012X
- Аннотация: We consider a hypersingular integral equation on a convex bounded set on the planewith an integral understood in the sense of Hadamard finite part. In particular, equations of thistype arise when solving the Neumann boundary value problem for the Laplace and Helmholtzequations on a flat screen in the case where the solution is sought in the form of a double layerpotential. To numerically solve the equation, we use a numerical scheme based on piecewiselinear approximation of the unknown function on a triangular conformal grid and the collocationmethod. The uniform convergence of numerical solutions to an exact solution on a grid whenthe maximum cell diameter tends to zero has been proven.
- Добавил в систему: Сетуха Алексей Викторович