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Numerical analysis of structure preserving Nyström methods for Hamiltonian systems

Pfeiffer, Andreas and Arnold, Martin (2005) Numerical analysis of structure preserving Nyström methods for Hamiltonian systems. Applied Numerical Mathematics, 53, pp. 391-408.

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Abstract

Energy conservation is an essential property of conservative mechanical systems that should be carried over to the numerical solution. Betsch and Steinmann proposed recently perturbed potentials to achieve energy conservation in the time integration of N-body problems by Galerkin methods. In the present paper this approach is generalised to Nyström methods for Hamiltonian systems. A detailed analysis shows that energy conservation by perturbed potential functions does not affect the feasibility and (high) order of convergence of Nyström methods. Symmetry and reversibility properties are left unchanged as well. The theoretical results are illustrated by numerical tests indicating clearly the benefits of energy conserving methods in long-term simulations.

Item URL in elib:https://elib.dlr.de/12246/
Document Type:Article
Additional Information:LIDO-Berichtsjahr=2005,
Title:Numerical analysis of structure preserving Nyström methods for Hamiltonian systems
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Pfeiffer, AndreasUNSPECIFIEDUNSPECIFIED
Arnold, MartinMartin Luther University Halle-WittenbergUNSPECIFIED
Date:2005
Journal or Publication Title:Applied Numerical Mathematics
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:53
Page Range:pp. 391-408
Status:Published
Keywords:Geometric integration, Hamiltonian system, Nyström methods, Galerkin methods, Collocation, Energy
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Transport
HGF - Program Themes:V SH - Verbesserung der Sicherheit im Verkehr (old)
DLR - Research area:Transport
DLR - Program:V SH - Verbesserung der Sicherheit im Verkehr
DLR - Research theme (Project):V - ViFa (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics (until 2012) > System Dynamics and Control (former Control Design Engineering)
Deposited By: DLR-Beauftragter, elib
Deposited On:20 Sep 2007
Last Modified:31 Jul 2019 19:15

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