Abstract
The paper presents comparison of several exact and approximate absorbing conditions, which are used to truncate computation domains of open (unbounded) initial boundary value problems of the electromagnetic theory of gratings. This comparison allows to judge the reliability and efficiency of absorbing conditions widely used in computational practice. The paper demonstrates that in cases, when resonant wave scattering is possible, only exact absorbing conditions allow to preserve the stability and convergence of computational schemes, and to provide a required level of accuracy in calculating the diffraction characteristics of open periodic resonators.