2021/06/17 by Assyr Abdulle, Abdulle, Assyr, Lia Gander +3
Chemistry · Engineering · Materials Science · #37M25 #65C30 #65L04 #65L20 #92C42 #Advanced Control Systems Optimization #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #Numerical Analysis (math.NA) #Thermal and Kinetic Analysis
paper · pdf · doi:10.48550/arxiv.2106.09339
openalex publication_date 2021/06/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this paper we propose a new discrete stochastic simulation algorithm: the postprocessed second kind stabilized orthogonal τ-leap Runge-Kutta method (PSK-τ-ROCK). In the context of chemical kinetics this method can be seen as a stabilization of Gillespie's explicit τ-leap combined with a postprocessor. The stabilized procedure allows to simulate problems with multiple scales (stiff), while the postprocessing procedure allows to approximate the invariant measure (e.g. mean and variance) of ergodic stochastic dynamical systems. We prove stability and accuracy of the PSK-τ-ROCK. Numerical experiments illustrate the high reliability and efficiency of the scheme when compared to other τ-leap methods.