Two-step runge-kutta methods with quadratic stability functions

D. Conte, R. D'Ambrosio, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions.We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.

Original languageEnglish (US)
Pages (from-to)191-218
Number of pages28
JournalJournal of Scientific Computing
Issue number2
StatePublished - Aug 2010


  • A-stability
  • Absolute stability
  • L-stability
  • Order conditions
  • Quadratic stability polynomials
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

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


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