[en] A numerical method for solving the 4D Schroedinger equation involving the time and three spatial coordinates is proposed. The method makes use of the partial coordinate splitting (PCS). The Hamiltonian in polar coordinates allows formal separation of radial and angular parts that leads to difficulties associated with the singularity of the angular part. The PCS principal idea is that in the vicinity of r=0 it is preferable not to split off the angular part at all. The method is applied to the calculation of the multi-fold differential cross section of the ionization of hydrogen atom and hydrogen molecular ion by fast electron impact. We propose a direct approach, which involves the reduction of the initial 6D Schroedinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics, thus avoiding the use of functions of the continuous spectrum of the ejected electron. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles