Published August 29, 1995
| Version public
Journal Article
The rate of error growth in Hamiltonian-conserving integrators
Creators
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1.
Georgia Institute of Technology
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2.
Stanford University
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.
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).Additional details
Identifiers
- Eprint ID
- 78159
- DOI
- 10.1007/BF01003559
- Resolver ID
- CaltechAUTHORS:20170613-104839336
Funding
- NSF
- DMS-9208684
- NSF
- INT-9302016
- Office of Naval Research (ONR)
- N00014-92-J-1876
- NSF
- DMS-9201727
Dates
- Created
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2017-06-13Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J30