Phase fitted variational integrators using interpolation techniques on non regular grids

  • The possibility of deriving a high order variational integrator that utilizes intermediate nodes within one time interval time to approximate the action integral is investigated. To this purpose, we consider time nodes chosen through linear or exponential expressions and through the roots of Chebyshev polynomial of the first kind in order to approximate the configurations and velocities at those nodes. Then, by defining the Lagrange function as a weighted sum over the discrete Lagrangians corresponding to the curve segments, we apply the phase fitted technique to obtain an exponentially fitted numerical scheme. The resulting integrators are tested for the numerical simulation of the planar tThe possibility of deriving a high order variational integrator that utilizes intermediate nodes within one time interval time to approximate the action integral is investigated. To this purpose, we consider time nodes chosen through linear or exponential expressions and through the roots of Chebyshev polynomial of the first kind in order to approximate the configurations and velocities at those nodes. Then, by defining the Lagrange function as a weighted sum over the discrete Lagrangians corresponding to the curve segments, we apply the phase fitted technique to obtain an exponentially fitted numerical scheme. The resulting integrators are tested for the numerical simulation of the planar two body problem with high eccentricity and of the three-body orbital motion within a solar system.show moreshow less

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Metadaten
Author:Odysseas T. Kosmas, Sigrid Leyendecker
URN:urn:nbn:de:bvb:29-opus-38459
Document Type:Article
Language:English
Date of Publication (online):2012/11/08
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Release Date:2012/11/08
Tag:exponential distribution; integral equations; interpolation; polynomials
SWD-Keyword:-
Original publication:AIP Conference Proceedings 1479 (2012): S. 2402-2406. 07.11.2012 <http://proceedings.aip.org/resource/2/apcpcs/1479/1/2402_1>
Institutes:Naturwissenschaftliche Fakultät / Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.60.-x Numerical approximation and analysis / 02.60.Ed Interpolation; curve fitting
Collections:Universität Erlangen-Nürnberg / Allianzlizenzen / Allianzlizenzen 2012

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