Invariant curves of one-step methods
This paper considers the invariant sets of numerical one-step integration methods in a neighbourhood of a hyperbolic periodic solution of a nonlinear ODE. Using results from the dynamical systems theory it was possible to show that for the usual one-step methods the invariant sets areCk-circles (closed curves) for small enough stepsizeh. Here we give a direct proof for that and also show that they areO(hp)Ck-close to the true periodic trajectory, wherep is the order of the method.
Subject classificationAMS 65L 34C
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