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dc.contributor.authorHuang, Weizhang
dc.contributor.authorLeimkuhler, Benedict J.
dc.date.accessioned2015-02-26T17:20:01Z
dc.date.available2015-02-26T17:20:01Z
dc.date.issued1997-01-01
dc.identifier.citationHuang, Weizhang & Leimkuhler, Benedict. "The adaptive Verlet method." SIAM J. Sci. Comput., 18(1), 239–256. (18 pages). http://dx.doi.org/10.1137/S1064827595284658.en_US
dc.identifier.urihttp://hdl.handle.net/1808/16881
dc.descriptionThis is the published version, also available here: http://dx.doi.org/10.1137/S1064827595284658.en_US
dc.description.abstractWe discuss the integration of autonomous Hamiltonian systems via dynamical rescaling of the vector field (reparameterization of time). Appropriate rescalings (e.g., based on normalization of the vector field or on minimum particle separation in an N-body problem) do not alter the time-reversal symmetry of the flow, and it is desirable to maintain this symmetry under discretization. For standard form mechanical systems without rescaling, this can be achieved by using the explicit leapfrog--Verlet method; we show that explicit time-reversible integration of the reparameterized equations is also possible if the parameterization depends on positions or velocities only. For general rescalings, a scalar nonlinear equation must be solved at each step, but only one force evaluation is needed. The new method also conserves the angular momentum for an N-body problem. The use of reversible schemes, together with a step control based on normalization of the vector field (arclength reparameterization), is demonstrated in several numerical experiments, including a double pendulum, the Kepler problem, and a three-body problem.en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.subjecttime-reversible methodsen_US
dc.subjectsymplectic methodsen_US
dc.subjectHamitonian systemsen_US
dc.subjectvariable stepsize methodsen_US
dc.subjectVerleten_US
dc.subjectleapfrongen_US
dc.subjectN-Body problemsen_US
dc.titleThe adaptive Verlet methoden_US
dc.typeArticle
kusw.kuauthorHuang, Weizhang
kusw.kudepartmentMathematicsen_US
dc.identifier.doi10.1137/S1064827595284658
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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