Regular Runge-Kutta pairs

D.J. Higham

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Time-stepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize Runge-Kutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded Runge-Kutta pairs used in variable stepsize mode with local error control. First, the limiting case of a zero error tolerance is considered. A recursive regularity test, based on the folding technique of Hairer, Iserles and Sanz-Serna (1990), is developed. It is then shown how regularity at zero tolerance carries through to the case of small tolerances. Finally, the property of regularity for all tolerances is characterized.
LanguageEnglish
Pages229-241
Number of pages12
JournalApplied Numerical Mathematics
Volume25
DOIs
Publication statusPublished - 1997

Fingerprint

Runge-Kutta
Tolerance
Regularity
Variable Step Size
Error Control
Zero
Time Stepping
Folding
Limiting
Fixed point

Keywords

  • Error control
  • Spurious fixed point
  • Variable time-stepping
  • mathematics
  • computer science

Cite this

Higham, D.J. / Regular Runge-Kutta pairs. In: Applied Numerical Mathematics. 1997 ; Vol. 25. pp. 229-241.
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Regular Runge-Kutta pairs. / Higham, D.J.

In: Applied Numerical Mathematics, Vol. 25, 1997, p. 229-241.

Research output: Contribution to journalArticle

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