NUMERICAL METHOD FOR COUPLING THE MACRO AND MESO SCALES IN STOCHASTIC CHEMICAL KINETICS

摘要

A numerical method is developed for simulation of stochastic chemical reactions. The system is modeled by the Fokker-Planck equation for the probability density of the molecular state. The dimension of the domain of the equation is reduced by assuming that most of the molecular species have a normal distribution with a small variance. The numerical approximation preserves properties of the analytical solution such as non-negativity and constant total probability. The method is applied to a nine dimensional problem modelling an oscillating molecular clock. The oscillations stop at a fixed point with a macroscopic model but they continue with our two dimensional, mixed macroscopic and mesoscopic model.