Energy conservation with non-symplectic methods: examples and counter-examples

DOI10.1007/s10543-004-5240-6zbMath1082.65132OpenAlexW2030112441MaRDI QIDQ2566635

Erwan Faou, Ernst Hairer, Truong-Linh Pham

Publication date: 26 September 2005

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://archive-ouverte.unige.ch/unige:12121

zbMATH Keywords

Hamiltonian systemsenergy conservationbackward error analysiscounter examplesnon-symplectic methodssymplectic one-step methods

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

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Cites Work

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• On the Butcher group and general multi-value methods
• The life-span of backward error analysis for numerical integrators
• Non-existence of the modified first integral by symplectic integration methods. II: Kepler problem
• Symmetric multistep methods over long times
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• Solving Ordinary Differential Equations I
• Order Conditions for Canonical Runge–Kutta Schemes
• Energy drift in reversible time integration
• An Algebraic Theory of Integration Methods
• Ergodicity and the Numerical Simulation of Hamiltonian Systems

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