Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation

Abstract

Numerical integration of stiff stochastic differential equations based on stochastic computational singular perturbation (SCSP) was recently developed in [62]. In this paper, a modified stochastic computational singular perturbation (MSCSP) method is considered. Similar to what was proposed in [26] for deterministic chemical reaction systems, the current study applies the sensitivity derivatives of the forcing terms with respect to the state variables to measure the reaction scales, which leads to a quasi-steady state equation for the fast species. This yields explicit large-step integrators for stochastic fast-slow stiff differential equations systems, which removes the expensive eigen-calculations of the standard SCSP integrators. The efficiency of the MSCSP integrators is demonstrated with the benchmark stochastic Davis-Skodje model and a nonlinear catalysis model under certain stochastic disturbances.