Niesen, J and Moan, PC (2014) On an asymptotic method for computing the modified energy for symplectic methods. Discrete and Continuous Dynamical Systems - Series A, 34 (3). 1105 - 1120. ISSN 1078-0947
Abstract
We revisit an algorithm by Skeel et al. [5,16] for computing the modified, or shadow, energy associated with symplectic discretizations of Hamiltonian systems. We amend the algorithm to use Richardson extrapolation in order to obtain arbitrarily high order of accuracy. Error estimates show that the new method captures the exponentially small drift associated with such discretizations. Several numerical examples illustrate the theory.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014, American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in American Institute of Mathematical Sciences following peer review. The definitive publisher-authenticated version Niesen, J and Moan, PC (2014) On an asymptotic method for computing the modified energy for symplectic methods. Discrete and Continuous Dynamical Systems - Series A, 34 (3). 1105 - 1120. ISSN 1078-0947 is available online at: DOI10.3934/dcds.2014.34.1105 |
Keywords: | Modified energy; symplectic integration; Hamiltonian systems; Richardson extrapolation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Feb 2015 14:10 |
Last Modified: | 26 Apr 2015 19:05 |
Published Version: | http://dx.doi.org/10.3934/dcds.2014.34.1105 |
Status: | Published |
Publisher: | American Institute of Mathematical Sciences |
Identification Number: | 10.3934/dcds.2014.34.1105 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83359 |