Operator splitting for chemical reaction systems with fast chemistry

Splitting methods are frequently used for large scale chemical reaction systems. The main reason is the reduced computational cost for solving the subproblems in comparison to the time integration of the full problem. However, a splitting error is introduced. The most popular splitting schemes are the first order Lie-Trotter splitting and the second order Strang splitting. However, in case of stiff differential equations the Strang splitting suffers from order reduction and both schemes have order one for stiff differential equations. Therefore, the step size restrictions due to the low order can result in a prohibitive small step size. Hence, splitting schemes with order larger than one are necessary for stiff differential equations. The Richardson extrapolation of the Lie-Trotter splitting is a second order scheme. In this paper we examine differential equations with a fast chemical source term and a slow transport term. Thus, all stiffness of the system is related to the chemical source term. We show that the Richardson extrapolation does not suffer from order reduction in this case. Furthermore, we perform a stability analysis of the extrapolated splitting scheme for a linear test problem. Thereby the operators of the test problem do not commute.