Boundary-value problems for the Helmholtz equation and their discrete mathematical models

We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically. © 2010 Springer Science+Business Media, Inc.