  The procedure for obtaining a difference equation, the solution of which is
the components of the electric (or magnetic) field at the chosen set of volume
points of the resonator chain, was developed. We started with the wave equation
with boundary conditions and obtained the difference equation without boundary
conditions. Boundary conditions were included into the coefficients of the
difference equation for the electric field. As the obtained equation connects
the field values in different points (in general case, on an infinite set of
points), the proposed procedure represents a nonlocal model for field
description. Solutions of the difference equation for the electric field were
analyzed. It was shown that they coincide with good accuracy with the ones that
were obtained by direct summing of relevant series.
