Comparison of Approximation Schemes in Stochastic Simulation Methods for Stiff Chemical Systems
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Date
2009-07-30T20:31:38Z
Authors
Wells, Chad R.
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Interest in stochastic simulations of chemical systems is growing. One of the aspects
of simulation of chemical systems that has been the prime focus over the past
few years is accelerated simulation methods applicable when there is a separation
of time scale. With so many new methods being developed we have decided to look
at four methods that we consider to be the main foundation for this research area.
The four methods that will be the focus of this thesis are: the slow scale stochastic
simulation algorithm, the quasi steady state assumption applied to the stochastic
simulation algorithm, the nested stochastic simulation algorithm and the implicit
tau leaping method. These four methods are designed to deal with stiff chemical
systems so that the computational time is decreased from that of the "gold
standard" Gillespie algorithm, the stochastic simulation algorithm.
These approximation methods will be tested against a variety of sti examples
such as: a fast reversible dimerization, a network of isomerizations, a fast species
acting as a catalyst, an oscillatory system and a bistable system. Also, these
methods will be tested against examples that are marginally stiff, where the time
scale separation is not that distinct.
From the results of testing stiff examples, the slow scale SSA was typically the
best approximation method to use. The slow scale SSA was highly accurate and
extremely fast in comparison with the other methods. We also found for certain
cases, where the time scale separation was not as distinct, that the nested SSA was
the best approximation method to use.