Higher Order Methods for Differential Inclusions

We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time interval. We provide formulas for the local error based on Lipschitz constants and bounds on higher-order derivatives. The method is based on a Fliess-like expansion, and extends previous results by providing error estimates which are valid for all possible inputs.