Solution of the Problem of Diffraction by a Circular Inhomogeneous Cylinder Partially Covered by a Reflective Screen

Based on the method of extended boundary conditions, an algorithm for the numerical solution of the two-dimensional problem of diffraction by a dielectric cylinder with wave number depending on the radial coordinate, which is partially covered by a perfectly reflective screen. The method is tested for the case of a homogeneous medium inside a dielectric cylinder. The accuracy of the fulfillment of the optical theorem is checked for various dependences of the wave number on the radial coordinate and the angular dependences of the scattering diagram are plotted for different opening angles of the reflective screen.