On rigorous and approximate nonstationary partial radiation conditions

When solving numerically hyperbolic equations in spatially unbounded region s, the volume of calculations can be reduced by using the radiation conditi ons. To this end, a bounded subregion with an imaginary boundary is formed in an original region. One solves an equation in this subregion looking for a solution which satisfies the radiation conditions on the imaginary bound ary. In this paper, a variant of these conditions is analyzed which substan tially reduces the RAM resources necessary for numerical implementation of the method. Since the proposed conditions are approximate, their applicatio n must be justified. First of all, it is necessary to analyze the existence and uniqueness of a solution to a problem in a bounded subregion and to pr ove its closeness to the solution to the original problem. These aspects ar e studied in this palter using the Klein-Gordon equation on a half-line, wh ich arises in the problems of electromagnetic scattering in waveguides.