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

Reshniak, Viktor; Khaliq, Abdul; Voss, David

doi:10.1016/j.cam.2019.03.044

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

Journal Article · Tue Apr 16 00:00:00 EDT 2019 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2019.03.044· OSTI ID:1665956

^[1]; Khaliq, Abdul ^[2]; Voss, David ^[3]

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)

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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1665956

Journal Information:: Journal of Computational and Applied Mathematics, Vol. 361, Issue 1; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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