Strong-stability-preserving additive linear multistep methods
Copyright policy )Strong-stability-preserving additive linear multistep methods
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.
23 pages, 3 figures
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Method of lines for initial value and initial-boundary value problems involving PDEs, 65L06, 65L05, 65M20, multistep methods, strong-stability-preserving scheme, ordinary differential equations, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Method of lines for initial value and initial-boundary value problems involving PDEs, 65L06, 65L05, 65M20, multistep methods, strong-stability-preserving scheme, ordinary differential equations, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations
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