Challenges in Geometric Numerical Integration

DOI10.1007/978-3-319-05254-0_10zbMath1325.65174OpenAlexW289387411MaRDI QIDQ2948979

Ernst Hairer

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-05254-0_10

zbMATH Keywords

algorithmHamiltonian systemslong-time behaviorFourier expansionsbackward error analysisnonlinear oscillatory problem

Mathematics Subject Classification ID

Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (2)

Symplectic waveform relaxation methods for Hamiltonian systems ⋮ Discrete embeddings for Lagrangian and Hamiltonian systems

Cites Work

• Energy separation in oscillatory Hamiltonian systems without any non-resonance condition
• Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. I
• The life-span of backward error analysis for numerical integrators
• Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. II
• 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
• Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
• Geometric Numerical Integration

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