Explicit Time Integration Methods Based on Simplified Stochastic Computational Singular Perturbation

Abstract

The research presented in this dissertation focuses on the development of efficient explicit time integration schemes for the chemical Langevin equations (CLEs). Due to the presence of multiple time scales in complex chemical reaction networks, CLEs often involve stiffness and hence classical explicit time integration methods require extremely small step sizes to maintain numerical stability. The methodology proposed in this research is based on the concept of stochastic computational singular perturbation, which separates the fast and slow dynamics of an underlying stiff stochastic differential equation system by projecting the drift and diffusion onto appropriate sets of basis. The CLE system can then be integrated forward in two steps, one for the slow dynamics and the other for the fast dynamics which can be approximated by a stochastic algebraic relation, and thus admits much larger step sizes than classical explicit schemes. The schemes are applied to a stiff chemical reaction system involving 3 species and 6 reaction channels. Numerical experiments show significant improvement in computational efficiency compared to classical explicit methods while maintaining numerical stability.