The splitting scheme for numerical integration of the collisionless Boltzmann equation, appropriate to spherical stellar systems is described. Both an equilibrium model (the Plummer model) and a nonequilibrium model (a uniform-density sphere) are tested. The results presented show that the scheme is stable and accurate. The evolution of the distribution function for the collapse of a uniform-density sphere has been reproduced in detail. It is found that in the core the velocity distribution after violent relaxation is not Maxwellian but partially degenerate.

Key words: Numerical experiments; Stellar dynamics; Violent relaxation.