Inertial manifolds and linear multi-step methods

We determine the existence and C1 convergence of an inertial manifold for a strongly A(α) stable, pth order, p≧1, linear multi-step method approximating a sectorial evolution equation that satisfies a gap condition. This inertial manifold gives rise to a one-step method that C1 approximates the inertial form of the evolution equation and yields further approximation properties of the multi-step method.