Dual series equations for wave diffraction by conical edge (Q2754702)

A method of dual series equations in Legendre functions for the scalar problem of diffraction on the cone with edge is considered. The method is based on correct transition to an infinite system of algebraic equations, using ``semiinversion'' for their regularization and obtaining solutions, that ensure fulfillment of all boundary conditions of the problem including the Meixner condition at the edge. A family of regularizing operators of the problem is constructed and those of them optimal for the numerical solution of the problem are selected. Approximate systems effective for the determination of the characteristics of the scattered field for cones of large dimensions are derived.