Numerical solution of scalar diffraction problems in integral statements on spectra of integral operators

Fredholm boundary integral equations of the first kind with a single unknown function are considered. Each equation is conditionally equivalent to a scalar diffraction (transmission) problem on a three-dimensional homogeneous inclusion and is solved numerically. A modified numerical method for solving the diffraction problem on the spectrum of an integral operator is proposed and tested in the case where the conditions for the correct solvability of the integral equation and its equivalence to the original problem are violated.