Monte Carlo simulation of spatially inhomogeneous coagulation of particles altogether with their diffusion

Monte Carlo algorithm for simulation of coagulation of particles altogether with their diffusion is developed. The problem to solve is the boundary-value problem for the 1D Smoluchowski equation containing convection and diffusion terms.
The stochastic particles method is underlying the algorithm. The principal features of the algorithm are the use of special Markov process and a splitting scheme according to physical processes.
A special technique to reduce the estimator variance is developed. The method of tentative estimation of the algorithm parameters is given.