A variable step-size selection method for implicit integration schemes

Raymond Holsapple, Ram Iyer, David Doman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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 languageEnglish
Title of host publicationProceedings of the 2006 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3013-3018
Number of pages6
ISBN (Print)1424402107, 9781424402106
DOIs
StatePublished - 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Conference

Conference2006 American Control Conference
CountryUnited States
CityMinneapolis, MN
Period06/14/0606/16/06

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    Holsapple, R., Iyer, R., & Doman, D. (2006). A variable step-size selection method for implicit integration schemes. In 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