Computation of integral manifolds for Carathéodory differential equations

We derive two numerical approximation schemes for local invariant manifolds of nonautonomous ordinary differential equations which can be measurable in time and Lipschitzian in the spatial variable. Our approach is inspired by previous work of Jolly, Rosa (2005), "Computation of non-smooth local center manifolds", IMA Journal of Numerical Analysis 25, 698-725, on autonomous ODEs and based on truncated Lyapunov-Perron operators. Both of our methods are applicable to the full hierarchy of strongly stable, stable, center-stable and the corresponding unstable manifolds, and exponential refinement strategies yield exponential convergence. Several examples illustrate our approach