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Numerical method for coupling the macro and meso scales in stochastic chemical kinetics. (English) Zbl 1137.65006
The authors develop a numerical method for simulation of stochastic chemical reaction system modeled by the Fokker-Planck equation for the probability density of the molecular state. Under the assumption that most of the molecular species have a normal distribution with a small variance, the dimension of the domain of the equation is reduced. The method preserves properties of the analytic solution such as non-negativity and constant total probability and is applied to a nine dimensional problem modeling an oscillating molecular clock.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
80A30 Chemical kinetics in thermodynamics and heat transfer
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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