New numerical-analytical methods in diffraction theory

This paper is aimed at presenting analytical and numerical-analytical methods developed by the authors to be employed in solving boundary value problems in mathematical physics and finding their application in diffraction theory. It was consistently realized that the idea of analytical regularization of ill-conditioned integral, integral-differential, and series equations of the first kind resulted in the efficient techniques and numerical algorithms which made it possible to solve these equations on the computer. The presented regularization techniques are successfully used in studies of two- and three-dimensional wavy scattering by closed and unclosed screens, compact and periodic, dielectric and perfectly conducting scatterers.