RECONSIDERING TRIGONOMETRIC INTEGRATORS

DOI10.1017/S1446181109000042zbMath1178.65142OpenAlexW2036083026MaRDI QIDQ3647122

Dion R. J. O'Neale, Robert I. Mclachlan

Publication date: 30 November 2009

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181109000042

zbMATH Keywords

performancenumerical integrationnumerical examplesinitial value problemsFermi-Pasta-Ulam problemtrigonometric integratorssymplectic algorithmshighly oscillatory Hamiltonian systems

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Numerical nonlinear stabilities in dynamical systems (65P40)

Related Items (1)

The averaged Lagrangian method

Cites Work

• Unnamed Item
• Derivation of simplectic numerical schemes for highly oscillatory Hamiltonian systems.
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A study of extrapolation methods based on multistep schemes without parasitic solutions
• A Gautschi-type method for oscillatory second-order differential equations
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Rigorous verification of trajectories for the computer simulation of dynamical systems
• Long-Time-Step Methods for Oscillatory Differential Equations
• Nonlinear Stability Analysis of Area-Preserving Integrators
• Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
• Error analysis of exponential integrators for oscillatory second-order differential equations

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