This paper is the latest version of the numerical-analytical algorithm for solving the forward seismic problem and migration. The main concept of the algorithm is in splitting of 2D and 3D seismic problems to a series of 1D problems with the help of the finite integral Fourier, Fourier-Bessel or Legendre transforms and with the use of a 1D finite difference technique. In this paper, instead of the finite difference method with respect to one spatial coordinate and time, we propose to use the finite difference approximation with respect to only the spatial coordinate with a subsequent analytical solution to the obtained system of ordinary differential equations with respect to time.