Analytic solutions and results of the numerical calculation of the one-component coagulation equation. The top panels (a), (b), and (c) are for the constant kernel, and the bottom panels (d), (e), and (f) are for the additive kernel. The left panels (a) and (d) were calculated with fiducial parameters N_bd = 16 (i.e., N = 241) and θ_c = 1; the middle panels (b) and (e) were calculated with a finer grid, N_bd = 40 (i.e., N = 601) and θ_c = 1; and the right panels (c) and (f) were calculated with a finer bin grouping, N_bd = 16 (i.e., N = 241) and θ_c = 0.1. In each plot, the sets of lines with four different colors show the snapshots at four different times. In each set, the lines show the tree method with the given θ_c and k_c = 1 000 000 (solid line), the direct method (dashed line), and the analytic solution (dotted line). All numerical results were calculated with adaptive time stepping.