Differential inclusions are mathematical models of nondeterministic continuous-time systems for which no stochastic information on the behavior is known. They arise naturally as reduced models of deterministic systems or as models of components of a distributed system with partial knowledge of the inputs. In order to verify that such systems satisfy safety specifications, we need to compute rigorous over-approximations to the set of reachable states. In this essay, we outline such a method, which gives high-order error for a single time step and a uniform bound on the error over the finite time interval. The approach is based on the approximations of inputs by finitely parametrized functions at each time step.keywordsdifferential inclusionsreachable setstochastic informationsingle step errorinput-affine systemsthese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.