On the convergence of the vortex loop method with regularization for the Neumann boundary value problem on a plane screen

G. V. Ryzhakov, A. V. Setukha

Результат исследований: Вклад в журналСтатьярецензирование

7 Цитирования (Scopus)

Аннотация

We consider a linear integral equation with a supersingular integral treated in the sense of the Hadamard finite value, which arises in the solution of the Neumann boundary value problem for the Laplace equation with the representation of the solution in the form of a doublelayer potential. We consider the case in which the exterior boundary value problem is solved outside a plane surface (a screen). For the integral operator in the above-mentioned equation, we suggest quadrature formulas of the vortex loop method with regularization, which provide its approximation on the entire surface when using an unstructured partition. In the problem in question, the derivative of the unknown density of the double-layer potential, as well as the errors of quadrature formulas, has singularities in a neighborhood of the screen edge. We construct a numerical scheme for the integral equation on the basis of the suggested quadrature formulas and prove an estimate for the norm of the inverse matrix of the resulting system of linear equations and the uniform convergence of the numerical solutions to the exact solution of the supersingular integral equation on the grid.

Язык оригиналаАнглийский
Страницы (с-по)1365-1371
Число страниц7
ЖурналDifferential Equations
Том47
Номер выпуска9
DOI
СостояниеОпубликовано - сент. 2011
Опубликовано для внешнего пользованияДа

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