Two-step Runge-Kutta: Theory and practice

S. Tracogna, Bruno Welfert

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

Local and global error for Two-Step Runge-Kutta (TSRK) methods are analyzed using the theory of B-series. Global error bounds are derived in both constant and variable stepsize environments. An embedded TSRK pair is constructed and compared with the RK5(4)6M pair of Dormand and Prince on the DETEST set of problems. Numerical results show that the TSRK performs competitively with the RK method.

Original languageEnglish (US)
Pages (from-to)775-799
Number of pages25
JournalBIT Numerical Mathematics
Volume40
Issue number4
DOIs
StatePublished - Dec 2000

Keywords

  • B-series
  • Embedded formula
  • Global error bounds
  • Local error estimation
  • Runge-Kutta methods
  • Two-Step Runge-Kutta methods
  • Variable step

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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