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.
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| 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). | ||||||||||||
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| 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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