Numerical method for coupling the macro and meso scales in stochastic chemical kinetics

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. Dedicated to the memory of Germund Dahlquist (1925–2005). AMS subject classification (2000)  65M20, 65M60