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The ion drag force on dust grains in a dusty plasma contributes significantly to the formation of equilibrium dust layers and void regions in radio-frequency discharges. In addition to the drag due to the direct collection of ions and to momentum transfer of ions in the electric field near grains, dust grains can also be subject to a drag force due to the effect of coherent waves, such as dust acoustic waves that can grow because of the drift of plasma ions relative to charged grains induced by an externally imposed electric field. Here, we examine wave drag due to unstable dust acoustic waves in a collisional dusty plasma using numerical simulations. We study the drag as a function of grain size as well as neutral-ion and neutral-dust collisions in both one-dimensional periodic systems, in which it is easier to study the instability properties per se, and in aperiodic configurations in order to assess effects associated with dust drag and void formation. For the parameter range considered, we find that in the absence of background collisions, the instability tends to saturate by trapping the plasma ions in the electrostatic waves, which does not affect the dust grains very much. Including ion-neutral collisions tends to suppress ion trapping, which in turn leads to larger wave amplitudes and trapping of the dust, resulting in significant drag on the dust grains. Inclusion of neutral-dust collisions leads to a grain size-dependent result, with the persistence of trapping of, and thus drag on, larger grains only. For the parameters of this study, the wave drag force is much larger than the ion drag usually considered.