# 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. 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
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