Formal energy of a symplectic scheme for Hamiltonian systems and its applications. I

DOI10.1016/0898-1221(94)90147-3zbMath0822.70012OpenAlexW4213034854MaRDI QIDQ1324404

V. Pereyra

Publication date: 24 May 1994

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(94)90147-3

zbMATH Keywords

existencepower seriesRunge-Kutta schemestep sizestep transition operator

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (14)

Energy and Quadratic Invariants Preserving Methods for Hamiltonian Systems With Holonomic Constraints ⋮ Multisymplectic Hamiltonian variational integrators ⋮ Is the formal energy of the mid-point rule convergent? ⋮ Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems ⋮ Symplectic methods for the Ablowitz-Ladik model ⋮ Modified equations for weakly convergent stochastic symplectic schemes via their generating functions ⋮ New high order symplectic integrators via generating functions with its application in many-body problem ⋮ Important aspects of geometric numerical integration ⋮ Structure-preserving algorithms for Birkhoffian systems ⋮ Symplectic wavelet collocation method for Hamiltonian wave equations ⋮ Symplectic methods for the nonlinear Schrödinger equation ⋮ High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods ⋮ Splitting K-symplectic methods for non-canonical separable Hamiltonian problems ⋮ Energy corrections in Hamiltonian dynamics simulations

Cites Work

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• Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
• Non-conservativity of traditional schemes for Liouville and contact systems
• The symplecticity of multi-step methods
• The necessary condition for a Runge-Kutta scheme to be symplectic for Hamiltonian systems
• Geodesic flows on compact surfaces -- as an application of Hamiltonian formalism
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators

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