Scalar wave diffraction from infinitely thin perfectly conducting circular ring

A new strong mathematically rigorous and numerically efficient method for solving the boundary value problem of scalar wave diffraction by an infinitely thin circular ring screen is proposed. The method is based on the combination of the orthogonal polynomials approach and the ideas of the methods of analytical regularization. As a result of the suggested regularization procedure, the initial boundary value problems was equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e., to an equation of the type (I+H)x=b, x, b∈l₂ in the space l₂ of square summable sequences. This equation was solved numerically by means of a truncation method with, in principle, any required accuracy