Relative convergence phenomenon arising in the solution of diffraction from strip grating on a dielectric slab

This note shows that it is necessary to exercise caution when solving certain boundary value problems using conventional numerical techniques, for instance, the moment method. This is demonstrated by considering the problem of diffraction by a strip grating on a dielectric slab and it is shown that the phenomenon of relative convergence [1],[2] occurs in the process of solution; that is, for a given numerical approximation of the kernel of the integral equation the most accurate solution is obtained for an optimum size, and not for the largest size of the matrix. A guide is provided for choosing this optimum size.