Abstract: Differential formalism gives a rapid convergence of accurate results even under conditions of propagation of several hundred spectral orders and grazing angles of incidence for the gratings with low groove-depth-to-groove-spacing ratio (h/d $VLS 1) which are typical for this wavelength region. In the same way it was found that the rigorous results on the region of low $delta@/d ratios under the short time of computation may also be done through the modified integral method. By way of the programs created on the base of integral equations, the results done through the differential method were repeated and a good coincidence with them was found. These data allow us to speak about the equivalence of both methods - integral and differential - and about the convergence of algorithms. !7
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