Explicit, time reversible, adaptive step size control
(2005) In SIAM Journal on Scientific Computing 26(6). p.1838-1851- Abstract
- Adaptive step size control is difficult to combine with geometric numerical integration. As classical step size control is based on "past" information only, time symmetry is destroyed and with it the qualitative properties of the method. In this paper we develop completely explicit, reversible, symmetry-preserving, adaptive step size selection algorithms for geometric numerical integrators such as the Stormer-Verlet method. A new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory. For integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and, in particular, the total energy for Hamiltonian systems. It has the same... (More)
- Adaptive step size control is difficult to combine with geometric numerical integration. As classical step size control is based on "past" information only, time symmetry is destroyed and with it the qualitative properties of the method. In this paper we develop completely explicit, reversible, symmetry-preserving, adaptive step size selection algorithms for geometric numerical integrators such as the Stormer-Verlet method. A new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory. For integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and, in particular, the total energy for Hamiltonian systems. It has the same excellent long-term behavior as that obtained when constant steps are used. With variable steps, however, both accuracy and efficiency are greatly improved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/226528
- author
- Hairer, E and Söderlind, Gustaf LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- backward error analysis, reversible, and reversible step size control, explicit, Hamiltonian systems, Stormer-Verlet method, symmetric methods, time reversible and, adaptive integration, geometric integration, perturbation theory
- in
- SIAM Journal on Scientific Computing
- volume
- 26
- issue
- 6
- pages
- 1838 - 1851
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000231357700002
- scopus:27844551675
- ISSN
- 1064-8275
- DOI
- 10.1137/040606995
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- b23073b3-306e-45c7-ba55-884a7eac889e (old id 226528)
- date added to LUP
- 2016-04-01 16:27:06
- date last changed
- 2022-02-27 21:18:45
@article{b23073b3-306e-45c7-ba55-884a7eac889e,
abstract = {{Adaptive step size control is difficult to combine with geometric numerical integration. As classical step size control is based on "past" information only, time symmetry is destroyed and with it the qualitative properties of the method. In this paper we develop completely explicit, reversible, symmetry-preserving, adaptive step size selection algorithms for geometric numerical integrators such as the Stormer-Verlet method. A new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory. For integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and, in particular, the total energy for Hamiltonian systems. It has the same excellent long-term behavior as that obtained when constant steps are used. With variable steps, however, both accuracy and efficiency are greatly improved.}},
author = {{Hairer, E and Söderlind, Gustaf}},
issn = {{1064-8275}},
keywords = {{backward error analysis; reversible; and reversible step size control; explicit; Hamiltonian systems; Stormer-Verlet method; symmetric methods; time reversible and; adaptive integration; geometric integration; perturbation theory}},
language = {{eng}},
number = {{6}},
pages = {{1838--1851}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Scientific Computing}},
title = {{Explicit, time reversible, adaptive step size control}},
url = {{http://dx.doi.org/10.1137/040606995}},
doi = {{10.1137/040606995}},
volume = {{26}},
year = {{2005}},
}