Comparison of Approximation Schemes in Stochastic Simulation Methods for Stiff Chemical Systems

[摘要] Interest in stochastic simulations of chemical systems is growing. One of the aspectsof simulation of chemical systems that has been the prime focus over the pastfew years is accelerated simulation methods applicable when there is a separationof time scale. With so many new methods being developed we have decided to lookat 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 stochasticsimulation algorithm, the quasi steady state assumption applied to the stochasticsimulation algorithm, the nested stochastic simulation algorithm and the implicittau leaping method. These four methods are designed to deal with stiff chemicalsystems so that the computational time is decreased from that of the ;;goldstandard;; Gillespie algorithm, the stochastic simulation algorithm.These approximation methods will be tested against a variety of stiexamplessuch as: a fast reversible dimerization, a network of isomerizations, a fast speciesacting as a catalyst, an oscillatory system and a bistable system. Also, thesemethods will be tested against examples that are marginally stiff, where the timescale separation is not that distinct.From the results of testing stiff examples, the slow scale SSA was typically thebest approximation method to use. The slow scale SSA was highly accurate andextremely fast in comparison with the other methods. We also found for certaincases, where the time scale separation was not as distinct, that the nested SSA wasthe best approximation method to use.

[发布机构] University of Waterloo

[关键词] Applied Mathematics