Analytic solutions and results of the numerical calculation of the two-component coagulation equation. The panel layout is the same as Fig. 6, with an additional integrated distribution panel for each case. The upper panel in each subplot (a) through (f) shows the two-dimensional distribution of mvn(m, v), with contour line levels of 10⁻¹⁶, 10⁻¹², 10⁻⁸, 10⁻⁴, and 1. The bottom panel in each subplot shows the one-dimensional distribution integrated over the secondary component (volume v) to get the distribution of m² n(m), to match Fig. 6. The panels show the snapshot at the end of the simulation, t = t_max. Three different colors show the three different schemes: the tree method with θ_c = 1 (blue contour lines), the direct method (red contour lines), and the analytic solution (monochromatic filled contour or grey line). For most cases, the contour lines of the direct method and the tree method overlap in the 2D plot.