How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm
dc.contributor.author | Viswanath, Divakar | en_US |
dc.date.accessioned | 2006-09-11T19:35:47Z | |
dc.date.available | 2006-09-11T19:35:47Z | |
dc.date.issued | 2002-03 | en_US |
dc.identifier.citation | Viswanath, Divakar; (2002). "How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm." Bit Numerical Mathematics 42(1): 194-205. <http://hdl.handle.net/2027.42/47958> | en_US |
dc.identifier.issn | 0006-3835 | en_US |
dc.identifier.issn | 1572-9125 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/47958 | |
dc.description.abstract | The Wisdom-Holman algorithm is an effective method for numerically solving nearly integrable systems. It takes into account the exact solution of the integrable part. If the nearly integrable system is the solar system, for example, the Wisdom-Holman algorithm uses the solution consisting of Keplerian orbits obtained when the interplanetary interactions are ignored. The effectiveness of the algorithm lies in its ability to take long timesteps. We use the Duffing oscillator and Kepler's problem with forcing to deduce how long those timesteps can be. For nearly Keplerian orbits, the timesteps must be at least six per orbital period even when the orbital eccentricity is zero. High eccentricity of the Keplerian orbits constrains the algorithm and forces it to take shorter timesteps. The analysis is applied to the solar system and other problems. | en_US |
dc.format.extent | 279719 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Swets & Zeitlinger ; Springer Science+Business Media | en_US |
dc.subject.other | Keplerian Orbits | en_US |
dc.subject.other | Nearly Integrable Systems | en_US |
dc.subject.other | Hamiltonian | en_US |
dc.subject.other | Ordinary Differential Equations | en_US |
dc.subject.other | Computational Mathematics and Numerical Analysis | en_US |
dc.subject.other | Mathematics, General | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Numeric Computing | en_US |
dc.title | How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Philosophy | en_US |
dc.subject.hlbsecondlevel | Computer Science | en_US |
dc.subject.hlbtoplevel | Humanities | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Departments of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/47958/1/10543_2004_Article_331186.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1023/A:1021934522015 | en_US |
dc.identifier.source | Bit Numerical Mathematics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.