The well—posedness of the formulation of diffraction problems reduced to Fredholm integral equations of the first kind with a smooth kernel

Abstract

The well-posedness of diffraction problems that are reduced to Fredholm integral equations of the first kind with a smooth kernel is analyzed. The auxiliary source method and the method of extended boundary conditions, both of which involve solution of Fredholm integral equations of the first kind with a smooth kernel, are applied to show for specific examples that algorithms of calculation of all physically significant quantities—the scattering pattern, the field at an arbitrary spatial point except current-carrier points, etc.—are quite stable and allow for computation of the aforementioned quantities with a preassigned accuracy.