Symbolic-Numeric Pipeline for Reachability Analysis of Differential Equations with B-Series

An in-progress pipeline based on B-series is proposed to solve reachability analysis of ordinary differential equations. First, a symbolic step generates a B-series and its associated truncation error. This later is symbolically optimized in order to reduce the over-estimation introduced by computation with sets. Finally, the B-series is evaluated with affine arithmetic and intervals to produce a guaranteed reachable tube.