Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
AN ADAPTED SYMPLECTIC INTEGRATOR FOR HAMILTONIAN PROBLEMS
View through CrossRef
In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is developed. We present explicity the symplecticity conditions for the new modified Runge–Kutta–Nyström method. Numerical results indicate that the new method is much more efficient than the "classical" symplectic Runge–Kutta–Nyström second algebraic order method introduced in Ref. 1.
World Scientific Pub Co Pte Lt
Title: AN ADAPTED SYMPLECTIC INTEGRATOR FOR HAMILTONIAN PROBLEMS
Description:
In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced.
This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions.
Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is developed.
We present explicity the symplecticity conditions for the new modified Runge–Kutta–Nyström method.
Numerical results indicate that the new method is much more efficient than the "classical" symplectic Runge–Kutta–Nyström second algebraic order method introduced in Ref.
1.
Related Results
Symplectic Bregman Divergences
Symplectic Bregman Divergences
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are de...
Floer homology for ????-symplectic manifolds
Floer homology for ????-symplectic manifolds
(English) In this thesis we investigate various aspects of the dynamics of Hamiltonian vector fields in singular symplectic manifolds. We concentrate on two questions: first, we in...
Hamiltonian Monte Carlo Method and Symplectic Geometry
Hamiltonian Monte Carlo Method and Symplectic Geometry
Hamiltonian Monte Carlo (HMC) method is an application of non-Euclidean geometry to inverse problems. It is a probabilistic sampling method with the basis of Hamiltonian dynamics. ...
Linear Hamiltonian Vector Fields on Lie Groups
Linear Hamiltonian Vector Fields on Lie Groups
Linear vector fields on Lie groups constitute a fundamental class of dynamical systems, as their flows are one-parameter subgroups of automorphisms and their infinitesimal behavior...
Recognition through and representability of symplectic capacities and squeezing of small sets
Recognition through and representability of symplectic capacities and squeezing of small sets
This thesis is about recognition of objects through symplectic capacities, representability of symplectic capacities as target-embedding capacities, and arbitrary symplectic squeez...
On Symplectic Self-Adjointness of Hamiltonian Operator Matrices
On Symplectic Self-Adjointness of Hamiltonian Operator Matrices
The symmetry of the spectrum and the completeness of the eigenfunction system of the Hamiltonian operator matrix have important applications in the symplectic Fourier expansion met...
Determination of Pressure-Temperature Conditions of Retrograde Symplectic Assemblages in Granulites and Amphibolites
Determination of Pressure-Temperature Conditions of Retrograde Symplectic Assemblages in Granulites and Amphibolites
Symplectites form during post-orogenic fast uplift processes in orogenic belts, and retrograde Symplectic assemblages mainly consist of plagioclase + quartz ± orthopyroxene ± clino...
Coarse-Graining Hamiltonian Systems Using WSINDy
Coarse-Graining Hamiltonian Systems Using WSINDy
Abstract
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interact...