Phase fitted variational integrators using interpolation techniques on non regular grids
Kosmas O, Leyendecker S (2012)
Publication Language: English
Publication Type: Conference contribution, Conference Contribution
Publication year: 2012
Publisher: American Institute of Physics
Pages Range: 2402-2406
Conference Proceedings Title: AIP Conference Proceedings
Event location: Kos, Greece
DOI: 10.1063/1.4756679
Abstract
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 two body problem with high eccentricity and of the three-body orbital motion within a solar system.
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APA:
Kosmas, O., & Leyendecker, S. (2012). Phase fitted variational integrators using interpolation techniques on non regular grids. In AIP Conference Proceedings (pp. 2402-2406). Kos, Greece, GR: American Institute of Physics.
MLA:
Kosmas, Odysseas, and Sigrid Leyendecker. "Phase fitted variational integrators using interpolation techniques on non regular grids." Proceedings of the International Conference of Numerical Analysis and Applied Mathematics, Kos, Greece American Institute of Physics, 2012. 2402-2406.
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