Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

Abstract
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.

Citation
Hadjimichael Y, Ketcheson DI, Lóczi L, Németh A (2016) Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size. SIAM Journal on Numerical Analysis 54: 2799–2832. Available: http://dx.doi.org/10.1137/15M101717X.

Acknowledgements
This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The work of the fourth author was partially supported by the grant TAMOP-4.2.2.A-11/1/KONV-2012-0012.

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM Journal on Numerical Analysis

DOI
10.1137/15M101717X

arXiv
1504.04107

Additional Links
http://epubs.siam.org/doi/10.1137/15M101717X

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