Results 11 to 20 of about 1,079 (166)
A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS [PDF]
The Astronomical Journal, 2010 Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits.
Quinn, T. +3 more
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Multiscale Geometric Integration of Deterministic and Stochastic Systems [PDF]
, 2011 In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators. For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been ...
Tao, Molei
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Symplectic groupoids for Poisson integrators
Journal of Geometry and Physics, 2023 We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a neighborhood of the unit manifold, that, in turn, give Poisson integrators.
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Anomaly in symplectic integrator [PDF]
Physics Letters A, 2007 6 pages, no ...
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, 2004 Variational integrators are a class of discretizations for mechanical systems which are derived by discretizing Hamilton's principle of stationary action.
West, Matthew
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Symplectic integrators for spin systems [PDF]
Physical Review E, 2014 We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in $\mathbb{R}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is $O(3)$-equivariant. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields an
Robert I. McLachlan +2 more
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Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis [PDF]
Logical Methods in Computer Science, 2012 We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, generalizes the domain of linear "templates" introduced by Manna ...
Assalé Adjé +2 more
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On the Nonlinear Stability of Symplectic Integrators [PDF]
BIT Numerical Mathematics, 2004 The paper deals mainly with the problem of achieving stability for symplectic numerical integrators by the mean of studying the topological equivalence of the level sets of the original Hamiltonian and those of the modified Hamiltonian associated to the numerical integrators.
Mclachlan, Robert Iain. +2 more
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Tuning Symplectic Integrators is Easy and Worthwhile [PDF]
Communications in Computational Physics, 2022 Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and execution time is minimal, while the performance improvements can be large.
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Fourth-order symplectic integration [PDF]
Physica D: Nonlinear Phenomena, 1990 Die Autoren behandeln die Integration der Hamiltonschen Gleichungen unter Anwendung einer expliziten Vierter-Ordnung-Methode. Diese bewahrt die Eigenschaft, daß eine zeitliche Entwicklung eines solchen Systems eine kanonische Transformation aus den Anfangsbedingungen bis zum Endzustand erhält.
Forest, E., Ruth, R.D.
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