High order strong stability preserving time discretizations

Sigal Gottlieb*, David Isaac Ketcheson, Chi Wang Shu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

210 Scopus citations

Abstract

Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution of hyperbolic partial differential equations with discontinuous solutions. SSP methods preserve the strong stability properties-in any norm, seminorm or convex functional-of the spatial discretization coupled with first order Euler time stepping. This paper describes the development of SSP methods and the connections between the timestep restrictions for strong stability preservation and contractivity. Numerical examples demonstrate that common linearly stable but not strong stability preserving time discretizations may lead to violation of important boundedness properties, whereas SSP methods guarantee the desired properties provided only that these properties are satisfied with forward Euler timestepping. We review optimal explicit and implicit SSP Runge-Kutta and multistep methods, for linear and nonlinear problems. We also discuss the SSP properties of spectral deferred correction methods.

Original languageEnglish (US)
Pages (from-to)251-289
Number of pages39
JournalJournal of Scientific Computing
Volume38
Issue number3
DOIs
StatePublished - Mar 1 2009

Keywords

  • High order accuracy
  • Multistep methods
  • Runge-Kutta methods
  • Spectral deferred correction methods
  • Strong stability preserving
  • Time discretization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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