@inproceedings{e7a876699d0345aeaf23867cec257f31,
title = "Certifying trajectories of dynamical systems",
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 = "Ball arithmetic, Certified integration, Dynamical systems, Multiple precision computations, Reliable computation, Taylor models",
author = "\{van der Hoeven\}, Joris",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 ; Conference date: 11-11-2015 Through 13-11-2015",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-32859-1\_44",
language = "English",
isbn = "9783319328584",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "520--532",
editor = "Kotsireas, \{Ilias S.\} and Rump, \{Siegfried M.\} and Yap, \{Chee K.\}",
booktitle = "Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers",
}