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We propose an approach for computing under-as well as over-approximations for the reachable sets of continuous systems which are defined by non-linear Ordinary Differential Equations (ODEs). Given a compact and connected initial set of states, described by a system of polynomial inequalities, we compute under-approximations of the set of states reachable over time. Our approach is based on a simple yet elegant technique to obtain an accurate Taylor model over-approximation for a backwarddoi:10.1109/fmcad.2014.6987596 dblp:conf/fmcad/RwthSA14 fatcat:x45nwtjbuze7tgzk73du4fgp3a