  We present a new numerical algorithm for the solution of coupled collisional
and collisionless systems, based on the block structured adaptive mesh and time
refinement strategy (AMR). We describe the issues associated with the
discretization of the system equations and the synchronization of the numerical
solution on the hierarchy of grid levels. We implement a code based on a higher
order, conservative and directionally unsplit Godunov's method for
hydrodynamics; a symmetric, time centered modified symplectic scheme for
collisionless component; and a multilevel, multigrid relaxation algorithm for
the elliptic equation coupling the two components. Numerical results that
illustrate the accuracy of the code and the relative merit of various
implemented schemes are also presented.
