Loading...
Numerical Shadowing Near Hyperbolic Trajectories
Van Vleck, Erik S.
Van Vleck, Erik S.
Citations
Altmetric:
Abstract
Shadowing is a means of characterizing global errors in the numerical solution of initial value ordinary differential equations by allowing for a small perturbation in the initial condition. The method presented in this paper allows for a perturbation in the initial condition and a reparameterization of time in order to compute the shadowing distance in the neighborhood of a periodic orbit or more generally in the neighborhood of an attractor. The method is formulated for one-step methods and both a serial and parallel implementation are applied to the forced van der Pol equation, the Lorenz equation and to the approximation of a periodic orbit.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/0916068.
Date
1995-04-05
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
Van Vleck, Erik. "Numerical Shadowing Near Hyperbolic Trajectories." (1995) SIAM J. Sci. Comput., 16(5), 1177–1189. (13 pages). http://dx.doi.org/10.1137/0916068.