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Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method

We show how stiffness manifests itself in the simulation of chemical reactions at both the continuous-deterministic level and the discrete-stochastic level. Existing discrete stochastic simulation methods, such as the stochastic simulation algorithm and the (explicit) tau-leaping method, are both exceedingly slow for such systems. We propose an implicit tau-leaping method that can take much larger time steps for many of these problems.