State-dependent symplecticity and area preserving numerical methods

DOI10.1016/J.CAM.2006.02.058zbMath1120.65130OpenAlexW2095990694MaRDI QIDQ885932

Donato Trigiante, Felice Iavernaro

Publication date: 14 June 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.02.058

zbMATH Keywords

Hamiltonian systemsRunge-Kutta methodsPoisson systemsdiscrete gradient methodssymplecticity

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (1)

The lack of continuity and the role of infinite and infinitesimal in numerical methods for ODEs: the case of symplecticity

Cites Work

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• Symmetric multistep methods over long times
• Backward error analysis for multistep methods
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Energy conservation with non-symplectic methods: examples and counter-examples
• Symmetric schemes and Hamiltonian perturbations of linear Hamiltonian problems
• Geometric integration using discrete gradients
• State Dependent Symplecticity of Symmetric Methods
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

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