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

Research output: Contribution to journalConference articleContributedpeer-review


  • Enrico Gerlach - , Chair of Astronomy, Lohrmann Observatory (Author)
  • Charalampos Skokos - , Max-Planck-Institute for the Physics of Complex Systems (Author)


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.


Original languageEnglish
Pages (from-to)475-484
Number of pages10
JournalDiscrete and continuous dynamical systems : DCDS Series A
Issue numberSuppl
Publication statusPublished - Sept 2011

External IDs

Scopus 84878202014



  • Chaos, Hénon-Heiles system, SALI method, Variational equations