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A systematic analysis of methods for computing the trajectories ofsolid-phase particles applied in modern astrophysics codes designed formodeling 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 thedust to the velocity of the gas t_{stop} is less than or comparable to therotation period, are considered. The methods are analyzed from the point ofview of their stability for computing the motions of small bodies, includingdust grains less than 1 micron, which are strongly coupled to the gas. Two testproblems are with analytical solutions. Fast first order accurate methods thatmake it possible to avoid additional restriction on the time step due to gasdrag in computations of the motion of grains of any size are presented. For theconditions of a circumstellar disks, the error in the velocity computationsobtained when using some stable methods become unacceptably large when the timestep size \tau>t_{stop}. For the radial migration of bodies that exhibit driftsalong nearly Keplerian orbits, an asymptotic approximation, sometimes calledthe short friction time approximation or drift flux model, gives a relativeerror for the radial velocity equals to St^2 where St is the Stokes number, theratio of the stopping time of the body to some fraction of the rotation period(dynamical time scale) in the disk.

Analysis of Methods for Computing the Trajectories of Dust Particles in a Gas-Dust Circumstellar Disk