Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Imre Fekete, Sidafa Conde, John N. Shadid

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2≤p≤4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability.

Original languageEnglish
Article number114325
JournalJournal of Computational and Applied Mathematics
Volume412
DOIs
StatePublished - 1 Oct 2022
Externally publishedYes

Keywords

  • Embedded pairs
  • Hyperbolic problems
  • Runge–Kutta methods
  • Step-size control
  • Strong stability preserving methods
  • Variable step-size

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