American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 475-484. doi: 10.3934/proc.2011.2011.475

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

Enrico Gerlach 1, and  Charlampos Skokos 2,

1. 

Lohrmann Observatory, Technical University Dresden, D-01062 Dredsen, Germany
2. 

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany

Received  July 2010 Revised  April 2011 Published  October 2011

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.
Keywords: SALI method, Variational equations, H´enon-Heiles system, chaos.
Mathematics Subject Classification: Primary: 37M25, 65P10; Secondary: 70H07, 37J99, 65P20.
Citation: Enrico Gerlach, Charlampos Skokos. Comparing the efficiency of numerical techniques for the integration of variational equations. Conference Publications, 2011, 2011 (Special) : 475-484. doi: 10.3934/proc.2011.2011.475
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