An Analysis of Operator Splitting Techniques in the Stiff Case

Operator splitting methods are commonly used in many applications. We focus here on the case where the evolution equations to be simulated are stiff. We will more particularly consider the case of two operators: a stiff one and a nonstiff one. This occurs in numerous application fields (e.g., combustion, air pollution, and reactive flows). The classical analysis of the splitting error may then fail, since the chosen splitting timestep Δt is in practice much larger than the fastest time scales: the asymptotic expansion Δt→0 is therefore no longer valid. We show here that singular perturbation theory provides an interesting framework for the study of splitting error. Some new results concerning the order of local errors are derived. The main result deals with the choice of the sequential order for the operators: the stiff operator must always be last in the splitting scheme.