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

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

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
Volume205
Issue number2
DOIs
StatePublished - Aug 15 2007

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Derivation of continuous explicit two-step Runge-Kutta methods of order three'. Together they form a unique fingerprint.

  • Cite this