Slowscale splitstep tauleap method for stiff stochastic chemical systems
Abstract
Tauleaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.
 Authors:

 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Middle Tennessee State Univ., Murfreesboro, TN (United States)
 Middle Tennessee State Univ., Murfreesboro, TN (United States)
 Western Illinois Univ., Macomb, IL (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1665956
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational and Applied Mathematics
 Additional Journal Information:
 Journal Volume: 361; Journal Issue: 1; Journal ID: ISSN 03770427
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Reshniak, Viktor, Khaliq, Abdul, and Voss, David. Slowscale splitstep tauleap method for stiff stochastic chemical systems. United States: N. p., 2019.
Web. doi:10.1016/j.cam.2019.03.044.
Reshniak, Viktor, Khaliq, Abdul, & Voss, David. Slowscale splitstep tauleap method for stiff stochastic chemical systems. United States. doi:10.1016/j.cam.2019.03.044.
Reshniak, Viktor, Khaliq, Abdul, and Voss, David. Tue .
"Slowscale splitstep tauleap method for stiff stochastic chemical systems". United States. doi:10.1016/j.cam.2019.03.044. https://www.osti.gov/servlets/purl/1665956.
@article{osti_1665956,
title = {Slowscale splitstep tauleap method for stiff stochastic chemical systems},
author = {Reshniak, Viktor and Khaliq, Abdul and Voss, David},
abstractNote = {Tauleaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.},
doi = {10.1016/j.cam.2019.03.044},
journal = {Journal of Computational and Applied Mathematics},
number = 1,
volume = 361,
place = {United States},
year = {2019},
month = {4}
}