Particle mass distribution for the high-resolution tests against the analytical solutions of the Smoluchowski equation (dotted lines) evaluated at different dimensionless times. We used 10⁴ representative particles and the merging parameter X = 0.01. We repeated each simulation ten times. Left: constant kernel K_ij = 1, evaluated at times 1, 10, 10², 10³, 10⁴, and 10⁵. Center: linear kernel $K_{ij}=\frac{1}{2}(m_i+m_j)$, evaluated at times 4, 8, 12, 16, and 20. Right: product kernel K_ij = m_i × m_j, evaluated at times 0.4, 0.7, and 0.9.