Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

Michał Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is A(α) -stable for some α∈ (0 , π/ 2 ]. Examples of highly stable IMEX GLMs are provided of order 1 ≤ p≤ 4. Numerical examples are also given which illustrate good performance of these schemes.

Original languageEnglish (US)
Pages (from-to)1105-1143
Number of pages39
JournalJournal of Scientific Computing
Issue number3
StatePublished - Mar 1 2017


  • Construction of highly stable methods
  • Convergence and stability analysis
  • General linear methods
  • IMEX methods
  • Inherent Runge–Kutta stability

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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