On High-Precision L∞ -stable IMEX Schemes for Scalar Hyperbolic Multi-scale Equations

Abstract

We present a framework to build high-accuracy IMEX schemes that fulfill the maximum principle, applied to a scalar hyperbolic multi-scale equation. Motivated by the findings in [5] that implicit R-K schemes are not L∞ -stable, our scheme, for which we can prove the L∞ stability, is based on a convex combination between a first-order and a class of second-order IMEX schemes. We numerically demonstrate the advantages of our scheme, especially for discontinuous problems, and give a MOOD procedure to increase the precision.