Implicit Second Order Weak Taylor Tau-Leaping Methods for the Stochastic Simulation of Chemical Kinetics

For biochemical systems, when some chemical species are represented by small numbers of molecules, discrete and stochastic approaches are more appropriate than continuous and deterministic approaches. The stochastic simulation algorithm (SSA), proposed by Gillespie, is a cardinal simulation method for the chemical kinetics. Because the SSA simulates every reaction event, the amount of the computational time is huge when models have many reaction channels and species. Therefore there have been many alternative algorithms whose goal is to improve the computational efficiency of the SSA. In this paper we use stochastic Taylor expansions to propose implicit second order weak Taylor tau-leaping methods for the stochastic simulation of chemical kinetics. These methods are motivated by the theory of weakly convergent discretizations of stochastic differential equations. Three different schemes of the second order weak Taylor tau-leaping methods are numerically tested to demonstrate the performance with accuracy