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The rate of error growth in Hamiltonian-conserving integrators

Estep, Donald J. and Stuart, Andrew M. (1995) The rate of error growth in Hamiltonian-conserving integrators. Zeitschrift für Angewandte Mathematik und Physik, 46 (3). pp. 407-418. ISSN 0044-2275. doi:10.1007/BF01003559. https://resolver.caltech.edu/CaltechAUTHORS:20170613-104839336

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Abstract

In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Hamiltonian. We show that the rate of growth of error is at most linear in time when such methods are applied to problems with period uniquely determined by the value of the Hamiltonian. This contrasts to generic numerical schemes, for which the rate of error growth is superlinear. Asymptotically, the rate of error growth for symplectic schemes is also linear. Hence, Hamiltonian-conserving schemes are competitive with symplectic schemes in this respect. The theory is illustrated with a computation performed on Kepler's problem for the interaction of two bodies.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF01003559DOIArticle
https://link.springer.com/article/10.1007/BF01003559PublisherArticle
http://rdcu.be/try6PublisherFree ReadCube access
Additional Information:© 1995 Birkhäuser Verlag. Received: August 29, 1994; revised: December 13, 1994. The work of D. J. Estep is supported by the National Science Foundation, contract numbers DMS-9208684 and INT-9302016. The work of A. M. Stuart is supported by the Office of Naval Research, contract number N00014-92-J-1876 and by the National Science Foundation, contract number DMS-9201727. We are grateful to an anonymous referee for helpful suggestions, particularly for drawing our attention to the result and proof outlined in Important Remark (iii).
Funders:
Funding AgencyGrant Number
NSFDMS-9208684
NSFINT-9302016
Office of Naval Research (ONR)N00014-92-J-1876
NSFDMS-9201727
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ30
Issue or Number:3
DOI:10.1007/BF01003559
Record Number:CaltechAUTHORS:20170613-104839336
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170613-104839336
Official Citation:Estep, D.J. & Stuart, A.M. Z. angew. Math. Phys. (1995) 46: 407. doi:10.1007/BF01003559
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78159
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Jun 2017 18:17
Last Modified:15 Nov 2021 17:37

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