We present an efficient numerical algorithm for simulating chemical kinetic
systems with multiple time scales. This algorithm is an improvement of the
traditional stochastic simulation algorithm (SSA), also known as
Gillespies algorithm. It is in the form of a nested SSA and uses an outer
SSA to simulate the slow reactions with rates computed from realizations
of inner SSAs that simulate the fast reactions. The algorithm itself is
quite general and seamless, and it amounts to a small modication of the
original SSA. Our analysis of such multi-scale chemical kinetic systems
allows us to identify the slow variables in the system, derive eective
dynamics on the slow time scale, and provide error estimates for the
nested SSA. Eciency of the nested SSA is discussed using these error
estimates, and illustrated through several numerical examples.
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