Explicit strong stability preserving multistep Runge–Kutta methods

Abstract
High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.

Citation
Bresten C, Gottlieb S, Grant Z, Higgs D, Ketcheson DI, et al. (2016) Explicit strong stability preserving multistep Runge–Kutta methods. Mathematics of Computation 86: 747–769. Available: http://dx.doi.org/10.1090/mcom/3115.

Acknowledgements
This research was supported by AFOSR grant number FA-9550-12-1-0224 and KAUST grant FIC/2010/05.

Publisher
American Mathematical Society (AMS)

Journal
Mathematics of Computation

DOI
10.1090/mcom/3115

Additional Links
http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03115-4/http://arxiv.org/pdf/1307.8058.pdf

Permanent link to this record