Van Vleck, Erik S.2015-04-022015-04-021995-04-05Van 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.https://hdl.handle.net/1808/17287This is the published version, also available here: http://dx.doi.org/10.1137/0916068.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.Article10.1137/0916068openAccess