Strong-stability-preserving additive linear multistep methods

Hadjimichael, Yiannis; Ketcheson, David

doi:10.1090/mcom/3296

Strong-stability-preserving additive linear multistep methods
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by Yiannis Hadjimichael and David I. Ketcheson PDF

Math. Comp. 87 (2018), 2295-2320 Request permission

Abstract:

The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain larger monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding nonadditive SSP linear multistep methods.

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