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

E. Gerlach | Zendy; Charlampos Skokos | Zendy

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

Author(s) -

E. Gerlach,

Charlampos Skokos

Publication year - 2011

Publication title -

conference publications

Language(s) - English

Resource type - Book series

DOI - 10.3934/proc.2011.2011.475

Subject(s) - quadratic equation , chaotic , mathematics , hamiltonian system , hamiltonian (control theory) , function (biology) , kinetic energy , computer science , mathematical optimization , mathematical analysis , classical mechanics , physics , geometry , artificial intelligence , evolutionary biology , biology

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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