Certifying Trajectories of Dynamical Systems

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

Abstract

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 “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 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire d’informatiqueUMR 7161 CNRS, Campus de l’École polytechniquePalaiseauFrance

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