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The simulation of chemical kinetics involving multiple scales constitutes amodeling challenge (from ordinary differential equations to Markov chain) and acomputational challenge (multiple scales, large dynamical systems, time steprestrictions). In this paper we propose a new discrete stochastic simulationalgorithm: the postprocessed second kind stabilized orthogonal $\tau$-leapRunge-Kutta method (PSK-$\tau$-ROCK). In the context of chemical kinetics thismethod can be seen as a stabilization of Gillespie's explicit $\tau$-leapcombined with a postprocessor. The stabilized procedure allows to simulateproblems with multiple scales (stiff), while the postprocessing procedureallows to approximate the invariant measure (e.g. mean and variance) of ergodicstochastic dynamical systems. We prove stability and accuracy of thePSK-$\tau$-ROCK. Numerical experiments illustrate the high reliability andefficiency of the scheme when compared to other $\tau$-leap methods.

Optimal explicit stabilized postprocessed $\tau$-leap method for the simulation of chemical kinetics