Accurate computations on inertial manifolds

An algorithm is implemented for the computation of inertial manifolds to ar bitrary accuracy. It is applied to the Kuramoto-Sivashinsky equation to rec over the high wave number components of elements on the global attractor. T he computational results demonstrate that this algorithm is significantly m ore accurate than previous methods, when compared after just a few iteratio ns. An essential feature of the algorithm is that it does not require that the entire manifold be constructed. Hence the algorithm is particularly sui ted for computing trajectories on the manifold, and its computational compl exity is independent of the dimension.