The splitting scheme for a numerical integration of the Vlasov equation is tested on one-dimensional problems with spatially periodic boundary conditions. The problems considered are (1) damping of small and large amplitude disturbances and (2) weak and strong Jeans instabilities, in an infinite homogeneous medium. These nonlinear phenomena are reproduced with high accuracy, efficiency, and stability. This suggests that the splitting scheme is applicable to sima1ations of more realistic stellar systems such as stellar disks and spherical stellar systems.

Key words: Jeans instability; Numerical experiments; Stellar dynamics; Vlasov equation.