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    Explicit strong stability preserving multistep Runge–Kutta methods

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    Type
    Article
    Authors
    Bresten, Christopher
    Gottlieb, Sigal
    Grant, Zachary
    Higgs, Daniel
    Ketcheson, David I. cc
    Németh, Adrian
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    KAUST Grant Number
    FIC/2010/05
    Date
    2015-10-15
    Online Publication Date
    2015-10-15
    Print Publication Date
    2016-06-02
    Permanent link to this record
    http://hdl.handle.net/10754/622747
    
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    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.
    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 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
    ae974a485f413a2113503eed53cd6c53
    10.1090/mcom/3115
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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