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We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method.
A class of methods for solving nonlinear simultaneous equations
C. G. Broyden · 1965
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On the construction and comparison of difference schemes
G. Strang · 1968
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Some convergence properties of Broyden’s method
D. M. Gay · 1979
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Stability of Runge-Kutta methods for trajectory problems
G. J. Cooper · 1987
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Higher-order hybrid Monte Carlo algorithms
M. Creutz and A. Gocksch · 1989
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Canonical integrators as tracking codes (or how to integrate perturbation theory with tracking)
E. Forest · 1989
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Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations
M. Suzuki · 1990
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Construction of higher order symplectic integrators
H. Yoshida · 1990
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Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear schrödinger equation
S. Dyachenko, A. Newell, A. Pushkarev, and V. Zakharov · 1992
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A Mathematical Introduction to Fluid Mechanics , volume 4 of Texts in Applied Mathematics
A. J. Chorin and J. E. Marsden · 1993
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Symplectic algorithm for constant-pressure molecular dynamics using a Nosé–Poincaré thermostat
J. B. Sturgeon and B. B. Laird · 2000
Cited alongside, same era.
The N N -vortex problem
P. K. Newton · 2001
Cited alongside, same era.
Symplectic maps for approximating polynomial Hamiltonian systems
S. Blanes · 2002
Cited alongside, same era.
Explicit symplectic integrator for s s -dependent static magnetic field
Y. K. Wu, E. Forest, and D. S. Robin · 2003
Cited alongside, same era.
Simulating Hamiltonian dynamics , volume 14 of Cambridge Monographs on Applied and Computational Mathematics
B. Leimkuhler and S. Reich · 2004
Cited alongside, same era.
Explicit geometric integration of polynomial vector fields
R. I. McLachlan and G. R. W. Quispel · 2004
Cited alongside, same era.
Explicit methods in extended phase space for inseparable Hamiltonian problems
P. Pihajoki · 2015
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Higher order explicit symmetric integrators for inseparable forms of coordinates and momenta
L. Liu, X. Wu, G. Huang, and F. Liu · 2016
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Modification of logarithmic Hamiltonians and application of explicit symplectic-like integrators
D. Li and X. Wu · 2017
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Explicit symplectic-like integrators with midpoint permutations for spinning compact binaries
J. Luo, X. Wu, G. Huang, and F. Liu · 2017
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Numerical Hamiltonian Problems
J. Sanz-Serna and M. Calvo · 2018
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On the order of convergence of Broyden’s method
F. Mannel · 2021
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
E. Hairer, C. Lubich, and G. Wanner · 2006
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Explicit symplectic integrators for solving nonseparable Hamiltonians
S. A. Chin · 2009
Cited alongside, same era.
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao · 2010
Cited alongside, same era.
Preservation of quadratic invariants by semiexplicit symplectic integrators for non-separable Hamiltonian systems
T. Ohsawa
Cited in the paper.
Explicit high-order symplectic integrators for charged particles in general electromagnetic fields
M. Tao
Cited in the paper.
Explicit symplectic approximation of nonseparable Hamiltonians: Algorithm and long time performance
M. Tao
Cited in the paper.
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Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
G. Pan, X. Wu, and E. Liang · 2021
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Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes
X. Wu, Y. Wang, W. Sun, and F. Liu · 2021
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A note on the construction of explicit symplectic integrators for Schwarzschild spacetimes
N. Zhou, H. Zhang, W. Liu, and X. Wu · 2022
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