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Attractive invariant manifolds for maps: Existence, smoothness and continuous dependence on the map
(1992)SAM Research ReportA global invariant manifold result for maps is derived with conditions that are easy to verify for applications. The result supplies existence and smoothness of the attractive manifold as well as additional useful properties. It is also shown that a Ck,1-perturbation of the map yields a Ck-perturbation of the manifold. Moreover, it is proved that if there is an attractive invariant manifold for the time-T map of an ODE then this manifold ...Report -
Invariant manifolds of numerical integration schemes applied to stiff systems of singular perturbation type - Part I: RK-methods
(1992)SAM Research ReportFor implicit RK-methods applied to singularly perturbed systems of ODEs it is shown that the resulting discrete systems preserve the geometric properties of the underlying ODE. As an application of this invariant manifold result sharp bounds on the global error are derived.Report