Grains mass distribution for the tests against the analytical solutions of the Smoluchowski equations (dashed lines) at different time instants: a) test against the constant kernel K_ik = 1, where 50 representative particles are simulated five times. The particles masses are binned and the distribution functions are averaged at dimensionless times t = 1,10,10²,10³,10⁴,10⁵. b) Test against the linear kernel . There are 150 particles used and the simulation is repeated five times. The distribution function is produced at times t = 4,8,12,16,20. c) Test against the product kernel K_ik = m_i × m_k. We use 400 representative particles and repeat the simulation ten times. The outputs are produced at times t = 0.4,0.7,0.9.