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A note on multistep methods and attracting sets of dynamical systems

Kloeden, P.E. and Lorenz, J. (1989) A note on multistep methods and attracting sets of dynamical systems. Numerische Mathematik, 56 (7). pp. 667-673.

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We consider a dynamical system described by an autonomous ODE with an asymptotically stable attractor, a compact set of orbitrary shape, for which the stability can be characterized by a Lyapunov function. Using recent results of Eirola and Nevanlinna [1], we establish a uniform estimate for the change in value of this Lyapunov function on discrete trajectories of a consistent, strictly stable multistep method approximating the dynamical system. This estimate can then be used to determine nearby attracting sets and attractors for the discretized system as done in Kloeden and Lorenz [3, 4] for 1-step methods.

Item Type: Journal Article
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Publisher: Springer New York
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