An analysis of operator splitting techniques in the stiff case Bruno Sportisse

Journal of Computational Physics, 161, 140-168, 2000

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 non stiff one. This occurs in numerous application fields (combustion, air pollution, reactive flows, ...). The classical analysis of the splitting error may then fail, since the chosen splitting timestep $\Delta{t}$ is in practice much larger than the fastest timescales: the asymptotic expansion $\Delta{t}\to{0}$ is therefore no longer valid.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 has always to be last in the splitting scheme.