Comparing the efficiency of numerical techniques for the integration of variational equations
arXiv:1008.1890
Abstract
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 Hénon-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.
arXiv comment12 pages, 7 figures, accepted for publication in the proceedings of the 8th AIMS International Conference
References in corpus (6)
- The Lyapunov Characteristic Exponents and their computation
- High order symplectic integrators for perturbed Hamiltonian systems
- Numerical integration of variational equations
- Quantum chaos in the nuclear collective model: I. Classical-quantum correspondence
- Symplectic integration of deviation vectors and chaos determination. Application to the Hénon-Heiles model and to the restricted three-body problem
- SALI: An Efficient Indicator of Chaos with Application to 2 and 3 Degrees of Freedom Hamiltonian Systems