  Four types of global error for initial value problems are considered in a
common framework. They include classical forward error analysis and shadowing
error analysis together with extensions of both to rescaling of time. To
determine the amplification of the local error that bounds the global error we
present a linear analysis similar in spirit to condition number estimation for
linear systems of equations. We combine these ideas with techniques for
dimension reduction of differential equations via a boundary value formulation
of numerical inertial manifold reduction. These global error concepts are
exercised to illustrate their utility on the Lorenz equations and inertial
manifold reductions of the Kuramoto-Sivashinsky equation.
