Higham, D.J.
(1997)
*Regular Runge-Kutta pairs.*
Applied Numerical Mathematics, 25.
pp. 229-241.
ISSN 0168-9274

## 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.

Item type: | Article |
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ID code: | 186 |

Keywords: | Error control, Spurious fixed point, Variable time-stepping, mathematics, computer science, Electronic computers. Computer science, Mathematics, Computational Mathematics, Applied Mathematics, Numerical Analysis |

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: | 10 Dec 2015 16:06 |

URI: | http://strathprints.strath.ac.uk/id/eprint/186 |

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