Strong-stability-preserving additive linear multistep methods

TL;DR

This paper extends the analysis of SSP linear multistep methods to problems with different stability conditions for each term, proposing optimal additive and perturbed methods that improve step sizes under certain conditions.

Contribution

It introduces a framework for analyzing SSP linear multistep methods with multiple stability conditions and develops optimal additive and perturbed methods within this context.

Findings

Optimal perturbed methods achieve larger step sizes with multiple conditions.

Optimal additive methods do not outperform non-additive SSP methods in step size.

The study extends SSP analysis to semi-discretized problems with varied stability constraints.

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 additive and perturbed 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 non-additive SSP linear multistep methods.