Explicit methods in extended phase space for inseparable Hamiltonian problems

DOI10.1007/s10569-014-9597-9zbMath1314.37060arXiv1411.3367OpenAlexW2092425184MaRDI QIDQ2348892

Pauli Pihajoki

Publication date: 16 June 2015

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3367

zbMATH Keywords

Hamiltonian systemsgeodesic equationvan der Pol oscillatornon-Hamiltonian systemsextended phase space methodsleapfrog integrationpartitioned Runge-Kutta

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (8)

Semiexplicit symplectic integrators for non-separable Hamiltonian systems ⋮ Preservation of Quadratic Invariants by Semiexplicit Symplectic Integrators for Nonseparable Hamiltonian Systems ⋮ Reliability of Lyapunov characteristic exponents computed by the two-particle method ⋮ Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian terms ⋮ Geodesic motions of test particles in a relativistic core-shell spacetime ⋮ On the construction of symmetric second order methods for ODEs ⋮ Numerical Methods and Closed Orbits in the Kepler–Heisenberg Problem ⋮ Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization

Uses Software

• LSODE
• SciPy

Cites Work

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• Explicit algorithmic regularization in the few-body problem for velocity-dependent perturbations
• A time-transformed leapfrog scheme. Integration of few-body systems with large mass ratios
• Explicit symplectic algorithms for time-transformed Hamiltonians
• Numerical treatment of ordinary differential equations by extrapolation methods
• Splitting methods
• Composition constants for raising the orders of unconventional schemes for ordinary differential equations
• Geometric Numerical Integration
• On Extrapolation Algorithms for Ordinary Initial Value Problems
• On the Construction and Comparison of Difference Schemes

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