On the nonlinear stability of symplectic integrators

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dc.contributor.authorMcLachlan, Robert I.
dc.contributor.authorPerlmutter, Matthew
dc.contributor.authorQuispel, G.R.W.
dc.date.accessioned2013-05-07T03:43:34Z
dc.date.available2013-05-07T03:43:34Z
dc.date.issued2001
dc.description.abstractThe modified Hamiltonian is used to study the nonlinear stability of symplectic integrators, especially for nonlinear oscillators. We give conditions under which an initial condition on a compact energy surface will remain bounded for exponentially long times for sufficiently small time steps. For example, the implicit midpoint rule achieves this for the critical energy surface of the H´enon- Heiles system, while the leapfrog method does not. We construct explicit methods which are nonlinearly stable for all simple mechanical systems for exponentially long times. We also address questions of topological stability, finding conditions under which the original and modified energy surfaces are topologically equivalent.en
dc.identifier.citationMcLachlan, R.I., Perlmutter, M., Quispel, G.R.W. (2001), On the nonlinear stability of symplectic integrators, Research Letters in the Information and Mathematical Sciences, 2, 93-107en
dc.identifier.issn1175-2777
dc.identifier.urihttp://hdl.handle.net/10179/4347
dc.language.isoenen
dc.publisherMassey Universityen
dc.subjectNonlinear oscillatorsen
dc.subjectNonlinear stabilityen
dc.subjectSymplectic Integratorsen
dc.titleOn the nonlinear stability of symplectic integratorsen
dc.typeArticleen
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