The Mathematical Institute, University of Oxford, Eprints Archive

Higher-order numerical methods for stochastic simulation of
chemical reaction systems

Székely Jr., T. and Burrage, K. and Erban, R. and Zygalakis, K. C. (2011) Higher-order numerical methods for stochastic simulation of
chemical reaction systems.
Journal of Chemical Physics . (Submitted)

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Abstract

In this paper, using the framework of extrapolation, we present an approach for obtaining higher-order -leap methods for the Monte Carlo simulation of stochastic chemical kinetics. Specifically, Richardson extrapolation is applied to the expectations of functionals obtained by a fixed-step -leap algorithm. We prove that this procedure gives rise to second-order approximations for the first two moments obtained by the chemical master equation for zeroth- and first-order chemical systems. Numerical simulations verify that this is also the case for higher-order chemical systems of biological importance. This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. We illustrate the results of a second extrapolation on two systems. The biggest barrier for observing higher-order convergence is the Monte Carlo error; we discuss different strategies for reducing it.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1428
Deposited By:Peter Hudston
Deposited On:11 Nov 2011 07:48
Last Modified:09 Feb 2012 13:55

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