Justification of an integro-functional method for diffraction problems in the presence of a half-space

In the present paper, we consider the discrete sources method as applied to the analysis of a scalar problem of the diffraction of a plane wave on a particle partly immersed in an absorbing half-space. The convergence of the method is proved with the use of a system of surface integral equations. We prove the Fredholm property of the obtained system and its unique solvability.