To the problem of diffraction by a half-line or a strip: diffraction of a cylindrical wave; calculation of the field on the coordinate plane

A new method is proposed for solving the diffraction problems with piecewise ideal boundaries. According to this method, the initial Helmholtz equation is substituted by a system of matrix equation of order 1. The coefficients of these equations are rational matrix functions of the coordinates. The properties of the coordinate matrix system are close to that of the ordinary differential equations, therefore the new method can be treated as a generalization of the separation of variables. The new technique is demonstrated on two examples: the Sommerfeld half-line problem and the strip problem