Symplectic phase flow approximation for the numerical integration of canonical systems

DOI10.1007/BF01385523zbMath0755.65074OpenAlexW2004561209MaRDI QIDQ1813048

Stefan Miesbach, Hans Josef Pesch

Publication date: 25 June 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133635

zbMATH Keywords

numerical resultscanonical systemsgenerating functionHamiltonian dynamical systemscanonical transformationsfourth-order methodRunge-Kutta-type methodslong time simulationsHenon-Heiles systemPoincaré invariantsaxisymmetric galaxysymplectic integration methods

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Celestial mechanics (70F15) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (5)

Symplectic algorithms based on the principle of least action and generating functions ⋮ New high order symplectic integrators via generating functions with its application in many-body problem ⋮ A Note on the Generating Function Method ⋮ On the role of invariants for the parameter estimation problem in Hamiltonian systems ⋮ A new class of symplectic integration schemes based on generating functions

Cites Work

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• Some properties of the discrete Hamiltonian method
• Runge-Kutta schemes for Hamiltonian systems
• Transversal homoclinic points and hyperbolic sets for non-autonomous maps. I
• Canonical Runge-Kutta methods
• Unconditionally stable methods for second order differential equations
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• Symplectic integration of Hamiltonian systems

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