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Higher Order Force Gradient Symplectic Algorithms

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1103/PhysRevE.62.8746
arXiv ID: physics/0006082
Source
arXiv
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Unknown
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Abstract

We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10 and 12, the new algorithms are approximately a factor of $10^3$, $10^4$, $10^4$ and $10^5$ better.

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