### Abstract

Implicit integration schemes, such as Runge-Kutta methods, are widely used in mathematics and engineering to numerically solve ordinary differential equations. Every integration method requires one to choose a step-size, h, for the integration. If h is too large or too small the efficiency of an implicit scheme is relatively low. As every implicit integration scheme has a global error inherent to the scheme, we choose the total number of computations in order to achieve a prescribed global error as a measure of efficiency of the integration scheme. In this paper, we propose the idea of choosing h by minimizing an efficiency function for general Runge-Kutta integration routines. We show the efficacy of this approach on some standard problems found in the literature.

Original language | English |
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Title of host publication | Proceedings of the 2006 American Control Conference |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3013-3018 |

Number of pages | 6 |

ISBN (Print) | 1424402107, 9781424402106 |

DOIs | |

State | Published - 2006 |

Event | 2006 American Control Conference - Minneapolis, MN, United States Duration: Jun 14 2006 → Jun 16 2006 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2006 |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2006 American Control Conference |
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Country | United States |

City | Minneapolis, MN |

Period | 06/14/06 → 06/16/06 |

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## Cite this

*Proceedings of the 2006 American Control Conference*(pp. 3013-3018). [1657179] (Proceedings of the American Control Conference; Vol. 2006). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2006.1657179