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How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm

dc.contributor.authorViswanath, Divakaren_US
dc.identifier.citationViswanath, Divakar; (2002). "How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm." Bit Numerical Mathematics 42(1): 194-205. <>en_US
dc.description.abstractThe 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.extent279719 bytes
dc.format.extent3115 bytes
dc.publisherKluwer Academic Publishers; Swets & Zeitlinger ; Springer Science+Business Mediaen_US
dc.subject.otherKeplerian Orbitsen_US
dc.subject.otherNearly Integrable Systemsen_US
dc.subject.otherOrdinary Differential Equationsen_US
dc.subject.otherComputational Mathematics and Numerical Analysisen_US
dc.subject.otherMathematics, Generalen_US
dc.subject.otherNumeric Computingen_US
dc.titleHow Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithmen_US
dc.subject.hlbsecondlevelComputer Scienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartments of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.identifier.sourceBit Numerical Mathematicsen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed

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