Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics  Project B3Numerical Analysis of equivariant evolution equations15052 Thorsten Hüls. We propose an algorithm for the approximation of stable and unstable fibers that applies to autonomous as well as to nonautonomous ODEs. The algorithm is based on computing the zerocontour of a specific operator; an idea that was introduced in [Hüls, 2014] for discrete time systems. We present precise error estimates for the resulting contour algorithm and demonstrate its efficiency by computing stable and unstable fibers for a (non)autonomous pendulum equation in two space dimensions. Our second example is the famous threedimensional Lorenz system for which several approximations of the twodimensional Lorenz manifold are calculated. In both examples, we observe an equally well performance for autonomous and nonautonomous chosen parameters.
