Extension of the Parabolic Equation Method in the Time Domain

The method of the parabolic equation was proposed by Mikhail A. Leontovich for calculate of radio propagation by an elementary source over the surface in 1944. Later, this method became widely used to solve the problems of propagation of acoustic and radio waves under difficult conditions. For example, it's used for such tasks as, the influence of the Earth's irregular surface on the radio propagation. The report attempts to modify the method of the parabolic equation for the possibility of solving problems in the time domain.