E.S. Van Vleck,

``Numerical Shadowing Near Hyperbolic Trajectories,''

(1995) SIAM J. Sci. Comp. 16 pp. 1177-1189.

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.