Uppsala University
Department of Information Technology

### Technical Report 2006-001

# Numerical Method for Coupling the Macro and Meso Scales in Stochastic Chemical Kinetics

### Lars Ferm and Per Lötstedt

January 2006

**Abstract:**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.

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