Higham, D.J. (1989) *Robust defect control with Runge-Kutta schemes.* SIAM Journal on Numerical Analysis, 26 (5). pp. 1175-1183. ISSN 0036-1429

## Abstract

Enright [Numerical Analysis Report 122, University of Manchester, Manchester, U.K., 1986] implements a Runge-Kutta method for solving the initial value problem using an alternative to the standard local error control scheme. The aim is to control the defect associated with a local interpolant by sampling its value at one or more fixed points within each step. However, in general, the quality of a sample point is problem-dependent and also varies from step to step. Two classes of interpolant are presented for which the asymptotic behaviour of the defect is known a priori, allowing optimal sample points to be chosen.

Item type: | Article |
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ID code: | 211 |

Keywords: | Runge-Kutta formula, defect, interpolation, numerical mathematics, Mathematics, Numerical Analysis |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Ms Sarah Scott |

Date Deposited: | 08 Mar 2006 |

Last modified: | 04 Sep 2014 09:52 |

URI: | http://strathprints.strath.ac.uk/id/eprint/211 |

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