Consistency and Stability of Tau-Leaping Schemes for Chemical Reaction Systems

We develop a theory of local errors for the explicit and implicit tau-leaping methods for simulating stochastic chemical systems, and we prove that these methods are first-order consistent. Our theory provides local error formulae that could serve as the basis for future stepsize control techniques. We prove that, for the special case of systems with linear propensity functions, both tau-leaping methods are first-order convergent in all moments. We provide a stiff stability analysis of the mean of both leaping methods, and we confirm that the implicit method is unconditionally stable in the mean for stable systems. Finally, we give some theoretical and numerical examples to illustrate these results.