Comparison of two-numerical methods for solving the problem of the diffraction of an $E$-polarized plane wave by an ideally conducting periodic surface

The method of collocation and the “integral equation” method, which is based on the use of the fast Fourier transform, are compared. The two algorithms are described and the results of numerical calculations of the surface currents and amplitudes of the non-decaying reflected plane waves obtained by the two methods are presented. Tables of the energy defects, the normalized difference of the solutions in $L_2[0,2\pi]$ and the times required to carry out calculations on a ES-1055 digital computer are given. The operation of the two algorithms is analysed.