Explicit strong stability preserving multistep Runge–Kutta methods
Type
ArticleAuthors
Bresten, ChristopherGottlieb, Sigal
Grant, Zachary
Higgs, Daniel
Ketcheson, David I.

Németh, Adrian
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
KAUST Grant Number
FIC/2010/05Date
2015-10-15Online Publication Date
2015-10-15Print Publication Date
2016-06-02Permanent link to this record
http://hdl.handle.net/10754/622747
Metadata
Show full item recordAbstract
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.Sponsors
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 ComputationAdditional Links
http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03115-4/http://arxiv.org/pdf/1307.8058.pdf
ae974a485f413a2113503eed53cd6c53
10.1090/mcom/3115