Scalar wave diffraction by a perfectly soft infinitely thin circular ring

A new strong mathematically rigorous and numerically effective method for solving the boundary value problem of scalar (for example acoustic) wave diffraction by a perfectly soft (Dirichlet boundary condition) infinitely thin circular ng is proposed. The method is based on the combination of the Orthogonal Polynomials Approach, and on the ideas of the methods of analytical regularization. As a result of the suggested regularization procedure, the initial boundary value problem is 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 in the space of l₂ square summable sequences. This equation can be solved numerically by means of the truncation method with, in principle, any required accuracy.