Derivation of continuous explicit two-step Runge-Kutta methods of order three

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.

Original languageEnglish (US)
Pages (from-to)764-776
Number of pages13
JournalJournal of Computational and Applied Mathematics
Issue number2
StatePublished - Aug 15 2007


  • Continuous interpolants
  • Nordsieck representation
  • Ordinary and delay differential equations
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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