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Title: Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Abstract

Tau-leaping 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:
ORCiD logo [1];  [2];  [3]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Middle Tennessee State Univ., Murfreesboro, TN (United States)
  2. Middle Tennessee State Univ., Murfreesboro, TN (United States)
  3. 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:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 361; Journal Issue: 1; Journal ID: ISSN 0377-0427
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. Slow-scale split-step tau-leap 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. Slow-scale split-step tau-leap method for stiff stochastic chemical systems. United States. doi:10.1016/j.cam.2019.03.044.
Reshniak, Viktor, Khaliq, Abdul, and Voss, David. Tue . "Slow-scale split-step tau-leap 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 = {Slow-scale split-step tau-leap method for stiff stochastic chemical systems},
author = {Reshniak, Viktor and Khaliq, Abdul and Voss, David},
abstractNote = {Tau-leaping 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}
}

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