On the numerical integration of FPU-like systems

DOI10.1016/j.physd.2010.11.008zbMath1208.37046OpenAlexW1989060178MaRDI QIDQ633721

Giancarlo Benettin, Antonio Ponno

Publication date: 29 March 2011

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2010.11.008

zbMATH Keywords

leap-frogbackward analysisgeometric numerical integrationFermi-pasta-Ulam

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

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Time-scales to equipartition in the Fermi-Pasta-Ulam problem: finite-size effects and thermodynamic limit ⋮ The Fermi-pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov exponents ⋮ Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions ⋮ HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS

Cites Work

• The Fermi-Pasta-Ulam problem: scaling laws vs. initial conditions
• On metastability in FPU
• From Hamiltonian perturbation theory to symplectic integrators and back
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• Numerical energy conservation for multi-frequency oscillatory differential equations
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
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