Higham, D.J. (1991) *Runge-Kutta defect control using Hermite-Birkhoff interpolation.* SIAM Journal on Scientific Computing, 12 (5). pp. 991-999. ISSN 1064-8275

Official URL: http://locus.siam.org/SISC/volume-12/art_0912053.h...

## Abstract

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstifi initial value problems were given in [D. J. Higham, SIAM J. Numer. Anal., 26(1989), pp. 1175-1183]. This work describes an alternative approach based on Hermite-Birkhofi interpolation. The new approach has two main advantages-it is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. For a particular Runge-Kutta formula the asymptotic analysis is verified numerically.

Item type: | Article |
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ID code: | 208 |

Keywords: | Runge–Kutta, defect, residual, backward error, Hermite–Birkhofi interpolation, numerical mathematics, Probabilities. Mathematical statistics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Ms Sarah Scott |

Date Deposited: | 09 Mar 2006 |

Last modified: | 26 Jul 2012 09:34 |

URI: | http://strathprints.strath.ac.uk/id/eprint/208 |

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