Higher Order Force Gradient Symplectic Algorithms

Details Higher Order Force Gradient Symplectic Algorithms Higher Order Force Gradient Symplectic Algorithms

2000-06-30

arxiv.org/abs/physics/0006082v1

Physics

Computational Physics

23 pages, 10 figures

Scientific paper

10.1103/PhysRevE.62.8746

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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