On high-precision L∞-stable IMEX schemes for scalar hyperbolic multi-scale equations
Abstract
We present a framework to build high-precision 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-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.
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