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G. Gottwald, M. Oliver, and N. Tecu,
Long-time accuracy for approximate slow manifolds in a finite
dimensional model of balance,
J. Nonlinear Sci. 17 (2007), 283-307.
Abstract:
We study the slow singular limit for planar anharmonic oscillatory
motion of a charged particle under the influence of a perpendicular
magnetic field when the mass of the particle goes to zero. This model
has been used by the authors as a toy model for exploring variational
high order approximations to the slow dynamics in rotating fluids. In
this paper, we address the long time validity of the slow limit
equations in the simplest nontrivial case. We show that the first
order reduced model remains O(ε) accurate over a long
1/ε time scale. The proof is elementary, but involves subtle
estimates on the nonautonomous linearized dynamics.
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