  A systematic analysis of methods for computing the trajectories of
solid-phase particles applied in modern astrophysics codes designed for
modeling gas-dust circumstellar disks has been carried out for the first time.
The motion of grains whose velocities are determined mainly by the gas drag,
that is, for which the stopping time or relaxation time for the velocity of the
dust to the velocity of the gas t_{stop} is less than or comparable to the
rotation period, are considered. The methods are analyzed from the point of
view of their stability for computing the motions of small bodies, including
dust grains less than 1 micron, which are strongly coupled to the gas. Two test
problems are with analytical solutions. Fast first order accurate methods that
make it possible to avoid additional restriction on the time step due to gas
drag in computations of the motion of grains of any size are presented. For the
conditions of a circumstellar disks, the error in the velocity computations
obtained when using some stable methods become unacceptably large when the time
step size \tau>t_{stop}. For the radial migration of bodies that exhibit drifts
along nearly Keplerian orbits, an asymptotic approximation, sometimes called
the short friction time approximation or drift flux model, gives a relative
error for the radial velocity equals to St^2 where St is the Stokes number, the
ratio of the stopping time of the body to some fraction of the rotation period
(dynamical time scale) in the disk.
