S.N. Chow and E.S. Van Vleck,

``Shadowing of Lattice Maps,''

(1994) Contemporary Mathematics 172 pp. 97-116.

ABSTRACT

The shadowing lemma provides an alternative means of characterizing global
errors. In this paper we study the shadowing properties of lattice maps,
typically discretizations of partial differential equations. Theoretical results are
presented that emphasize the relationship between exponential dichotomy and
the shadowing property. A simple algorithm for determining the shadowing
distance numerically is applied to the logistic map, the Henon map, a
discretization of Burgers' equation and a discretization of the Korteweg-de
Vries equation.