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pro vyhledávání: '"numerical integrators"'
Autor:
Andrews, Boris D., Farrell, Patrick E.
Numerical methods for the simulation of transient systems with structure-preserving properties are known to exhibit greater accuracy and physical reliability, in particular over long durations. These schemes are often built on powerful geometric idea
Externí odkaz:
http://arxiv.org/abs/2407.11904
Autor:
Ye, Xuda, Zhou, Zhennan
We propose a novel discrete Poisson equation approach to estimate the statistical error of a broad class of numerical integrators for the underdamped Langevin dynamics. The statistical error refers to the mean square error of the estimator to the exa
Externí odkaz:
http://arxiv.org/abs/2405.06871
We derive and analyze numerical methods for weak approximation of underdamped (kinetic) Langevin dynamics in bounded domains. First-order methods are based on an Euler-type scheme interlaced with collisions with the boundary. To achieve second order,
Externí odkaz:
http://arxiv.org/abs/2404.16584
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the
Externí odkaz:
http://arxiv.org/abs/2401.14800
Autor:
Laurent, Adrien
The aromatic bicomplex is an algebraic tool based on aromatic Butcher trees and used in particular for the explicit description of volume-preserving affine-equivariant numerical integrators. The present work defines new tools inspired from variationa
Externí odkaz:
http://arxiv.org/abs/2307.07984
Publikováno v:
Journal of Computational Dynamics Vol. 11, No. 1, January 2024, pp. 92-107
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such
Externí odkaz:
http://arxiv.org/abs/2308.08261
We study the convergence rate of discretized Riemannian Hamiltonian Monte Carlo on sampling from distributions in the form of $e^{-f(x)}$ on a convex body $\mathcal{M}\subset\mathbb{R}^{n}$. We show that for distributions in the form of $e^{-\alpha^{
Externí odkaz:
http://arxiv.org/abs/2210.07219
Publikováno v:
SIAM Journal on Numerical Analysis, 1998 Apr 01. 35(2), 586-599.
Externí odkaz:
https://www.jstor.org/stable/2587145
Autor:
Reich, Sebastian
Publikováno v:
SIAM Journal on Numerical Analysis, 1999 Jan 01. 36(5), 1549-1570.
Externí odkaz:
https://www.jstor.org/stable/2587170
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