Majorant frequency principle for an approximate solution of a nonlinear spatially inhomogeneous coagulation equation by the Monte Carlo method

We propose an efficient algorithm in the direct statistical simulation method for an approximate solution to the Cauchy problem for a nonlinear spatially inhomogeneous coagulation equation that describes the coagulation of particles together with their diffusion transfer. The use of the majorant frequency principle allows one to attain a linear dependence of the computational costs of the algorithm on the initial number of test particles. The main properties of the algorithm include a special markovian random process and a splitting scheme with respect to physical processes.

We consider in detail the spatially one-dimensional case of the above equation. For this case, we develop a special procedure for transforming the ensemble of test particles and propose a method for the preliminary estimation of the parameters of the computational algorithm.