Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Nonlinear Dynamics II
DY 26.5: Vortrag
Mittwoch, 16. März 2011, 17:30–17:45, ZEU 255
Algorithms for the integration of variational equations of multidimensional Hamiltonian systems — Enrico Gerlach1, Siegfried Eggl2, and •Charalampos Skokos3 — 1Lohrmann Observatory, Technical University Dresden, D-01062 Dresden, Germany — 2Institute for Astronomy, University of Vienna, Türkenschanzstrasse 17,A-1180 Vienna, Austria — 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany
We investigate the efficiency of different algorithms for the integration of the variational equations of multidimensional Hamiltonian systems. In particular we consider the tangent map (TM) method (Skokos Ch. and Gerlach E., 2010, PRE, 82, 036704 - Gerlach E. and Skokos Ch., 2010, arXiv:nlin.CD/1008.1890), a scheme based on symplectic integration techniques, as well as non-symplectic schemes, like the DOP853 general-purpose integrator and methods based on Taylor and Lie expansions. The numerical verification of well-known properties of chaos indicators like the Lyapunov Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs) is used for characterizing the efficiency of the various integration schemes. Besides discussing the methods theoretically, we will apply them exemplarily to the Fermi-Pasta-Ulam (FPU) β lattice model and to an astronomical N body problem to demonstrate the differences between them regarding parameters of practical importance, as e.g. CPU time requirements and reliability of the results.