This paper concerns the reliable integration of dynamical systems with a focus on the computation of one specific trajectory for a given initial condition at high precision. We describe several algorithmic tricks which allow for faster parallel computations and better error estimates. We also introduce so called “Lagrange models”. These serve a similar purpose as the more classical Taylor models, but we will show that they allow for larger step sizes, especially when the truncation orders get large.

Keywords: reliable computation, dynamical systems, certified integration, ball arithmetic, Taylor models, multiple precision computations

A.M.S. subject classification: 65G20, 37-04

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Corrected version: Pdf-2018