The Influence of the Asymptotic Regime on the RS-IMEX

Abstract

In this work, we investigate the performance and explore the limits of a novel implicit-explicit splitting [6] for the efficient treatment of singularly perturbed ODEs. We consider a singularly perturbed ODE where, based on the choice of initial conditions, the unperturbed equation does not necessarily describe the behavior of the perturbed one accurately. For the splitting presented in [6], this has a tremendous influence as it explicitly depends on the solution to the unperturbed equation. That this indeed poses a problem is shown numerically; but also the remedy of using the ’correct’ asymptotics is presented. Comparisons with a fully implicit and a standard implicit-explicit splitting are shown.