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.
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