Making big steps in trajectories

TL;DR

This paper introduces a novel high-precision algorithm for computing trajectories in hybrid systems, especially near discontinuities, outperforming traditional ODE solvers in accuracy within similar computation times.

Contribution

The paper presents a new algorithm for trajectory computation in hybrid systems using exact real arithmetic, enhancing precision near discontinuities.

Findings

Algorithm achieves higher precision than standard ODE solvers

Applicable to holomorphic flow functions in hybrid systems

Demonstrated with prototype implementation

Abstract

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time.