# Optimal explicit stabilized postprocessed $\\tau$-leap method for the simulation of chemical kinetics

Source: [Optimal explicit stabilized postprocessed $\\tau$-leap method for the simulation of chemical kinetics](<https://www.sota2.com/research/paper/68fa58311e209131ce9abe4a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:17:49.585Z

Authors: Assyr Abdulle, Lia Gander, Giacomo Rosilho de Souza

Published: 2021-06-17T09:20:49.000Z

## Abstract

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 $\\tau$-leap Runge-Kutta method (PSK-$\\tau$-ROCK). In the context of chemical kinetics this method can be seen as a stabilization of Gillespie's explicit $\\tau$-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-$\\tau$-ROCK. Numerical experiments illustrate the high reliability and efficiency of the scheme when compared to other $\\tau$-leap methods.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2106.09339>)

[PDF](<https://arxiv.org/pdf/2106.09339.pdf>)