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Stochastic algorithms for solving Smolouchovsky equation governing the coagulation processes are constructed. The derivation of the method is based on the interrelation between the Boltzmann type nonlinear equations and the Kolmogorov linear equation for the Markov processes. The justification is proposed under the molecule chaos hypothesis. We discuss three different stochastic algorithms: the Bird, Nanbu and a weight algorithms. To carry out a carefull numerical test of the methods proposed, we constructed a deterministic finite element method. A series of calculations confirm the efficiency of the stochastic algorithms. We solved also some applied problems related to the aerosol formation processes.

Stochastic algorithms for solving Smolouchovsky coagulation equation and applications to aerosol growth simulation.