Strong stability preserving implicit–explicit transformed general linear methods

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We consider the class of implicit–explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving (SSP) property, while the implicit part of the method has inherent Runge–Kutta stability (IRKS) property, and it is A-, or L-stable. We will also investigate the absolute stability of these methods when the implicit and explicit parts interact with each other. In particular, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A(α)-stable for α∈[0,π∕2]. Finally we furnish examples of SSP IMEX GLMs up to the order p=4 and stage order q=p with optimal SSP coefficients.

Original languageEnglish (US)
Pages (from-to)206-225
Number of pages20
JournalMathematics and Computers in Simulation
Volume176
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

  • Construction of highly stable methods
  • General linear methods
  • IMEX methods
  • Inherent Runge–Kutta stability
  • SSP property
  • Stability analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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