leapfrog integrator

E898982

geometric numerical integrator numerical integration method symplectic integrator

A leapfrog integrator is a symplectic numerical method for solving Hamiltonian dynamics that conserves energy well over long simulations, making it especially useful in physics and Hamiltonian Monte Carlo.

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All labels observed (1)

Label	Occurrences
leapfrog integrator canonical	1

Statements (48)

Predicate	Object
instanceOf	geometric numerical integrator ⓘ numerical integration method ⓘ symplectic integrator ⓘ
advantageOver	non‑symplectic integrators for long‑time Hamiltonian simulation ⓘ
appliedTo	separable Hamiltonians ⓘ
approximates	Hamiltonian flow ⓘ
assumes	Hamiltonian separable into kinetic and potential energy ⓘ
comparedTo	Runge–Kutta methods NERFINISHED ⓘ
enables	high acceptance rates in Hamiltonian Monte Carlo ⓘ
hasAlternativeName	Störmer–Verlet integrator NERFINISHED ⓘ leapfrog method NERFINISHED ⓘ
hasOrder	2 ⓘ
hasProperty	conditionally stable ⓘ explicit method ⓘ good long‑term energy conservation ⓘ second‑order accurate ⓘ symplectic ⓘ time‑reversible ⓘ volume‑preserving in phase space ⓘ
hasStepStructure	full‑step position update ⓘ half‑step momentum update ⓘ half‑step momentum update at end of step ⓘ
isSpecialCaseOf	partitioned Runge–Kutta method ⓘ second‑order symplectic Runge–Kutta–Nyström method ⓘ
minimizes	long‑term energy drift ⓘ
numericalErrorType	bounded energy error over long times ⓘ
preserves	phase‑space volume ⓘ symplectic structure ⓘ
relatedTo	Störmer–Verlet method NERFINISHED ⓘ Verlet integration NERFINISHED ⓘ position Verlet integrator NERFINISHED ⓘ velocity Verlet integrator NERFINISHED ⓘ
requires	choice of time step ⓘ
tradeoff	smaller time step improves accuracy but increases cost ⓘ
typicalUseContext	Bayesian computation ⓘ Markov chain Monte Carlo NERFINISHED ⓘ classical mechanics ⓘ computational physics ⓘ
usedFor	Hamiltonian Monte Carlo NERFINISHED ⓘ Hybrid Monte Carlo NERFINISHED ⓘ N‑body simulations in astrophysics ⓘ long‑time integration of Hamiltonian systems ⓘ molecular dynamics simulations ⓘ solving Hamiltonian dynamics ⓘ
usedIn	galactic dynamics simulations ⓘ lattice quantum chromodynamics simulations ⓘ planetary orbit integration ⓘ rigid‑body dynamics ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hamiltonian Monte Carlo → typicallyUses → leapfrog integrator ⓘ