On the numerical solution of a complete two-dimensional hypersingular integral equation by the method of discrete singularities

摘要

We study the solvability of a complete two-dimensional linear integral equation with a hypersingular integral understood in the sense of the Hadamard principal value. We justify the convergence of a quadrature-type numerical method for the case in which the equation in question is uniquely solvable. We present an application of the results to the numerical solution of the Neumann boundary value problem on a plane screen for the Helmholtz equation by the surface potential method.