Regular Runge-Kutta pairs

Higham, D.J. (1997) Regular Runge-Kutta pairs. Applied Numerical Mathematics, 25. pp. 229-241. ISSN 0168-9274 (http://dx.doi.org/10.1016/S0168-9274(97)00062-7)

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.

ORCID iDs

Higham, D.J. ORCID: https://orcid.org/0000-0002-6635-3461

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• Item metadata

  Item type:	Article
  ID code:	186
  Dates:	Date Event 1997 Published
  Subjects:	Science > Mathematics > Electronic computers. Computer science Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Ms Sarah Scott
  Date deposited:	02 Mar 2006
  Last modified:	11 Nov 2024 08:12
  URI:	https://strathprints.strath.ac.uk/id/eprint/186