Iterative Semi-implicit Splitting Methods for Stochastic Chemical Kinetics

In this paper, we present splitting methods that are based on iterative schemes and applied to stochastic models for chemical kinetics. The motivation arose of solving chemical kinetics with respect to stochastic influences in their models. The parameters and variables that describe the concentrations are based on extending the deterministic models to stochastic models. Such an extension is important to simulate the uncertainties of the concentrations. For the modelling equations, we deal with stochastic differential equations and it is important to extend the deterministic methods to stochastic methods. Here, we consider iterative splitting methods, based on Picard’s successive approximations, to solve the underlying stochastic differential equations. The benefit of relaxation behaviour of the iterative solvers is also obtained in the stochastic method and based on the stochastic process we obtain 1/2 of the accuracy as for the deterministic method, which is also given for non-iterative methods. We present the numerical analysis of the schemes and verified the results in numerical experiments of different chemical reaction systems.

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