Stochastic projective methods for simulating stiff chemical reacting systems

In this paper, stochastic projective methods are proposed to improve the stability and efficiency in simulating stiff chemical reacting systems. The efficiency of existing explicit tau-leaping methods can often severely be limited by the stiffness in the system, forcing the use of small time steps to maintain stability. The methods presented in this paper, namely stochastic projective (SP) and telescopic stochastic projective (TSP) method, can be considered as more general stochastic versions of the recently developed stable projective numerical integration methods for deterministic ordinary differential equations. SP and TSP method are developed by fully re-interpreting and extending the key projective integration steps in the deterministic regime under a stochastic context. These new stochastic methods not only automatically reduce to the original deterministic stable methods when applied to simulating ordinary differential equations, but also carry the enhanced stability property over to the stochastic regime. In some sense, the proposed methods are stochastic generalizations to their deterministic counterparts. As such, SP and TSP method can adopt a much larger effective time step than is allowed for explicit tau-leaping, leading to noticeable runtime speedup. The explicit nature of the proposed stochastic simulation methods relaxes the need for solving any coupled nonlinear systems of equations at each leaping step, making them more efficient than the implicit tau-leaping method with similar stability characteristics. The efficiency benefits of SP and TSP method over the implicit tau-leaping is expected to grow even more significantly for large complex stiff chemical systems involving hundreds of active species and beyond.