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

Pages: 475 - 484, Issue Special, September 2011

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Enrico Gerlach - Lohrmann Observatory, Technical University Dresden, D-01062 Dredsen, Germany (email)
Charlampos Skokos - Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany (email)

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 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:  Variational equations, chaos, SALI method, H´enon-Heiles system
Mathematics Subject Classification:  Primary: 37M25, 65P10; Secondary: 70H07, 37J99, 65P20

Received: July 2010;      Revised: April 2011;      Published: October 2011.