Rigorous error bounds for RK methods in the proof of chaotic behaviour

摘要

Complicated dynamical systems can be rigorously analysed by means of Conley index theory. Due to its partly numerical nature such an analysis necessitates bounds on the truncation and the round-off error. These are provided for explicit RK methods in the form of iteration schemes ready-made for applications. The presentation is aimed to simplify error bounds already available so that different error sources can be clearly overlooked. As an immediate application, a computer-assisted analysis elucidates the intricate dynamics of a simple mechanical system.