﻿ OPUS 4 | Phase fitted variational integrators using interpolation techniques on non regular grids

## 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.

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Author: Odysseas T. Kosmas, Sigrid Leyendecker urn:nbn:de:bvb:29-opus-38459 Article English 2012 Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) 2012/11/08 exponential distribution; integral equations; interpolation; polynomials - AIP Conference Proceedings 1479 (2012): S. 2402-2406. 07.11.2012 Naturwissenschaftliche Fakultät / Naturwissenschaftliche Fakultät -ohne weitere Spezifikation- Naturwissenschaften und Mathematik / Physik / Physik 00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.60.-x Numerical approximation and analysis / 02.60.Ed Interpolation; curve fitting open_access Universität Erlangen-Nürnberg / Allianzlizenzen / Allianzlizenzen 2012

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