Accurate computations on inertial manifolds

An algorithm is implemented for the computation of inertial manifolds to arbitrary accuracy. It is applied to the Kuramoto-Sivashinsky equation to recover the high wave number components of elements on the global attractor. The computational results demonstrate that this algorithm is significantly more accurate than previous methods, when compared after just a few iterations. An essential feature of the algorithm is that it does not require that the entire manifold be constructed. Hence the algorithm is particularly suited for computing trajectories on the manifold, and its computational complexity is independent of the dimension.