A numerical algorithm for obtaining the discrete ordinates solution of the time—dependent multigroup neutron and γ–ray transport equation with pulsed sources is discussed. The Adaptive Weighted Diamond Differenced scheme (AWDD scheme) and the S2rebalance method for accelerating inner iterations, consistent with the discretization of the transport equation, are described. The spectral analysis of stability of the WDD scheme is presented. Special tools for correct treatment of the time—dependent problems with pulsed sources are provided. The results of calculations of some benchmark problems given by B. D. Ganopol et al. are presented.