Results 121 to 130 of about 1,079 (166)

Integrable symplectic maps

Physica D: Nonlinear Phenomena, 1991
The paper first reviews the concept of a symplectic map, its characterization and properties and various ways of construction. Among these is a rather formal discrete version of Euler-Lagrange equations, which relates to earlier work by Maeda on discrete Hamiltonian and Lagrangian systems.
BRUSCHI M, RAGNISCO, Orlando, SANTINI PM, TU GZ   +3 more
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Extrapolation of symplectic Integrators

Celestial Mechanics and Dynamical Astronomy, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Blanes, S., Casas, F., Ros, J.
openaire   +1 more source

A Symplectic Integrator for Riemannian Manifolds

Journal of Nonlinear Science, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Leimkuhler, B., Patrick, G. W.
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Variable time step integration with symplectic methods

Applied Numerical Mathematics, 1997
Symplectic methods for Hamiltonian systems are known to have favourable properties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variables instead of quadratic growth, correct ...
E. Hairer, Hairer, Ernst
exaly   +2 more sources

Third-order symplectic integration method with inverse time dispersion transform for long-term simulation

Journal of Computational Physics, 2016
The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations ...
Yingjie Gao, Jinhai Zhang
exaly   +2 more sources

Exponentially fitted symplectic integrator

Physical Review E, 2003
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed.
T E, Simos, Jesus, Vigo-Aguiar
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Symplectic Integration with Processing: A General Study

SIAM Journal on Scientific Computing, 1999
Symplectic integration with processing is studied. More specifically the authors investigate the number of conditions required by the operators \(K\) and \(P\) in symplectic integrators with processing, given by \(e^{P} e^{-h K} e^{-P}\). The above number is determined for a Hamiltonian of the form \(H=A+B\).
Sergio Blanes, Fernando Casas, José Ros
openaire   +1 more source

Energy preserving symplectic integrators

Journal of Numerical Mathematics, 2011
Summary: Three one-parameter, eighth-order families of symplectic integrators are presented. They are based on the Strang splitting, the Forest-Ruth construction, and the Zassenhaus formula, respectively. In each time-step, a free parameter is adopted to preserve energy exactly in this step.
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Symplectic integrators: An introduction

American Journal of Physics, 2005
Symplectic integrators very nearly conserve the total energy and are particularly useful when treating long times. We demonstrate some of the properties of these integrators by exploring the structure of first-, second-, and fourth-order symplectic integrators and apply them to the simple harmonic oscillator.
Denis Donnelly, Edwin Rogers
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On correctors of symplectic integrators

Chinese Astronomy and Astrophysics, 2003
Abstract An intensive discussion is given here with numerical illustration on the symplectic correctors proposed by Wisdom et al. (1996). A simple method is given for deriving the first and second order correctors of any symplectic integrators in terms of Lie series for the general case, in which the Hamiltonian can be separated into a main ...
null Wu Xin, null Huang Tian-yi, null Wan Xiao-sheng   +2 more
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