dorsal/arxiv
View SchemaHigher Order Force Gradient Symplectic Algorithms
| Authors | Siu A. Chin, Donald W. Kidwell |
|---|---|
| Categories | |
| ArXiv ID | physics/0006082 |
| URL | https://arxiv.org/abs/physics/0006082 |
| DOI | 10.1103/PhysRevE.62.8746 |
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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"abstract": "We show that a recently discovered fourth order symplectic algorithm, which\nrequires one evaluation of force gradient in addition to three evaluations of\nthe force, when iterated to higher order, yielded algorithms that are far\nsuperior to similarly iterated higher order algorithms based on the standard\nForest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the\nstep-size independent error functions associated with energy conservation and\nthe rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric\nKepler problem. For orders 6, 8, 10 and 12, the new algorithms are\napproximately a factor of $10^3$, $10^4$, $10^4$ and $10^5$ better.",
"arxiv_id": "physics/0006082",
"authors": [
"Siu A. Chin",
"Donald W. Kidwell"
],
"categories": [
"physics.comp-ph",
"physics.space-ph"
],
"doi": "10.1103/PhysRevE.62.8746",
"title": "Higher Order Force Gradient Symplectic Algorithms",
"url": "https://arxiv.org/abs/physics/0006082"
},
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