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Hybrid method for the chemical master equation. (English) Zbl 1126.80010
Summary: The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate equations and the probability distribution for the stochastic variables satisfy a master equation. The probability distribution is obtained by the stochastic simulation algorithm due to Gillespie. The equations are coupled via a summation over the mesoscale variables. This summation is approximated by quasi-Monte Carlo methods. The error in the approximations is analyzed. The hybrid method is applied to three chemical systems from molecular cell biology.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80A32 Chemically reacting flows
65C05 Monte Carlo methods
65H10 Numerical computation of solutions to systems of equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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
Algorithm 823
Full Text: DOI
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