Exact solution (solid lines) and two numerical solutions (circles and squares, respectively) of the dustybox at x = 0.25, relaxing towards the barycenter velocity (dotted line) over six damping times (t = 0.06). Equivalently, t ≈ 3t_s,d, where t_s,d = ρ_d / K_d ≈ 0.02 is the stopping time. Numerical solutions of the first-order implicit drag solver are computed in the stiff regime (Δt = t_s,d = 0.02, squares) and in the non-stiff regime (Δt = 0.05t_s,d = 10^–3, circles).