Comparing the efficiency of numerical techniques for the integration of variational equations

Details Comparing the efficiency of numerical techniques for the integration of variational equations Comparing the efficiency of numerical techniques for the integration of variational equations

2010-08-11

arxiv.org/abs/1008.1890v2

Nonlinear Sciences

Chaotic Dynamics

12 pages, 7 figures, accepted for publication in the proceedings of the 8th AIMS International Conference

Scientific paper

We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta, and whose potential is a function of the generalized positions. We apply the various techniques to the well-known H\'enon-Heiles system, and use the Smaller Alignment Index (SALI) method of chaos detection to evaluate the percentage of its chaotic orbits. The accuracy and the speed of the integration schemes in evaluating this percentage are used to investigate the numerical efficiency of the various techniques.

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