  A rigorous convergence analysis of the Strang splitting algorithm for
Vlasov-type equations in the setting of abstract evolution equations is
provided. It is shown that under suitable assumptions the convergence is of
second order in the time step \tau. As an example, it is verified that the
Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this
analysis. Also, numerical experiments for the latter case are presented.
