The Influence of the Asymptotic Regime on the RS-IMEX
In this work, we investigate the performance and explore the limits of a novel implicit-explicit splitting (Kaiser and Schütz, A high-order method for weakly compressible flows. Commun. Comput. Phys. 22(4): 1150–1174, 2017) 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 Kaiser and Schütz, (A high-order method for weakly compressible flows. Commun. Comput. Phys. 22(4): 1150–1174, 2017), 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.
We thank Peter de Maesschalck for fruitful discussions. The first author has been partially supported by the German Research Foundation (DFG) project NO 361/3-3, and the University of Hasselt in the framework of the BOF 2016.
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