This article is cited in 1 paper

MATHEMATICS

Investigation of an approximate solution of some classes of surface integral equations of the first kind

E. H. Khalilov

Department of General and Applied Mathematics of the Azerbaijan State Oil and Industry University, Baku, Azerbaijan

Abstract: A sequence is constructed that converges to an exact solution of a hypersingular integral equation of the first kind of the external Neumann boundary value problem for the Helmholtz equation, which is the boundary value of the solution of the external Neumann boundary value problem on the boundary of the domain. In addition, a sequence is constructed that converges to an exact solution of a weakly singular integral equation of the first kind of the external Dirichlet boundary value problem for the Helmholtz equation, which is the boundary value of the normal derivative of the solution of the external Dirichlet boundary value problem on the boundary of the domain.

Keywords: integral equation of the first kind, weakly singular integral equations, hypersingular integral equations, Helmholtz equation, exterior Neumann boundary-value problem, exterior Dirichlet boundary-value problem.

UDC: 517.2; 519.64

MSC: 45E05; 31B10

Received: 08.07.2021

DOI: 10.17223/19988621/74/5

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