In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric...

algebra Symplectic integrator Symplectic manifold Symplectic matrix Symplectic representation Symplectic vector space, a vector space with a symplectic bilinear...

Because of its time-reversibility, and because it is a symplectic integrator, leapfrog integration is also used in Hamiltonian Monte Carlo, a method for...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

differential equations that arises in classical mechanics. It is a symplectic integrator and hence it yields better results than the standard Euler method...

restitution. Courant–Friedrichs–Lewy condition Energy drift Symplectic integrator Leapfrog integration Beeman's algorithm Verlet, Loup (1967). "Computer "Experiments"...

\omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally...

lemma for the numerical method to solve differential equations, see Symplectic integrator Split (disambiguation) Splitter (disambiguation) This disambiguation...

Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics...

conserving properties of the simulated Hamiltonian dynamic when using a symplectic integrator. The reduced correlation means fewer Markov chain samples are needed...