The Circular of the Holland Academy in the Hollander

The Circular of the Holland Academy which appeared in English in The Hollander, the English edition. The resolutions made at the Particular Synod of Chicago on April 29 and 30 are printed in full. A very informative and important document.https://digitalcommons.hope.edu/vrp_1850s/1007/thumbnail.jp

Numerical Shadowing Near Hyperbolic Trajectories

This 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