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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Explicit strong stability preserving multistep Runge–Kutta methods
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by Christopher Bresten, Sigal Gottlieb, Zachary Grant, Daniel Higgs, David I. Ketcheson and Adrian Németh PDF
Math. Comp. 86 (2017), 747-769 Request permission

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.
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Additional Information
  • Christopher Bresten
  • Affiliation: Department of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth, Massachusetts 02747
  • Email: cbresten@umassd.edu
  • Sigal Gottlieb
  • Affiliation: Department of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth, Massachusetts 02747
  • MR Author ID: 358958
  • Email: sgottlieb@umassd.edu
  • Zachary Grant
  • Affiliation: Department of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth Massachusetts 02747
  • Email: zgrant@umassd.edu
  • Daniel Higgs
  • Affiliation: Department of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth, Massachusetts 02747
  • MR Author ID: 906696
  • David I. Ketcheson
  • Affiliation: King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia
  • Adrian Németh
  • Affiliation: Department of Mathematics and Computational Sciences, Széchenyi István University, Győr, Hungary
  • Received by editor(s): September 3, 2014
  • Received by editor(s) in revised form: July 2, 2015, and September 18, 2015
  • Published electronically: June 2, 2016
  • Additional Notes: This research was supported by AFOSR grant number FA-9550-12-1-0224 and KAUST grant FIC/2010/05
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 747-769
  • MSC (2010): Primary 65M20
  • DOI: https://doi.org/10.1090/mcom/3115
  • MathSciNet review: 3584547