Stochastic particle approximations for Smoluchowski's coagulation equation (Q1872430)

A new Markov jump process approximating solutions of the coagulation equations has been introduced. A stochastic algorithm with reduced variance is proposed for the numerical treatment of the coagulation equation. Its convergence behavior is investigated when the number of particles in the stochastic particle system goes to infinity. Under suitable assumptions on the coagulation kernel, the limit is the unique solution of the coagulation equation. That conforms with the classical Marcus-Lushnikov theory. Detailed numerical experiments are performed to test the applicability and efficiency of the algorithm. In addition to illustrating standard theoretical results, new insights were provided to the gelation phenomenon. The algorithm shows a considerable efficiency gain if compared to the standard simulation method.