Drift-preserving numerical integrators for stochastic Hamiltonian systems

C Chen, D Cohen, R D'Ambrosio, A Lang - Advances in Computational …, 2020 - Springer
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems
with additive noise. For such problems, the expected value of the total energy, along the …

Numerical conservation issues for the stochastic Korteweg–de Vries equation

R D'Ambrosio, S Di Giovacchino - Journal of Computational and Applied …, 2023 - Elsevier
In this paper, we focus on structure-preserving issues for the numerical solution of the
stochastic Korteweg–de Vries equation, via stochastic ϑ-methods. It is well-known that the …

[图书][B] Symplectic integration of stochastic hamiltonian systems

J Hong, L Sun - 2022 - Springer
As numerous modern challenges in scientific questions, industrial needs, and societal
requirements emerge, the demand for designing numerical methods to solve tremendously …

[HTML][HTML] Strong backward error analysis of symplectic integrators for stochastic Hamiltonian systems

R D'Ambrosio, S Di Giovacchino - Applied Mathematics and Computation, 2024 - Elsevier
Backward error analysis is a powerful tool in order to detect the long-term conservative
behavior of numerical methods. In this work, we present a long-term analysis of symplectic …

Curved schemes for stochastic differential equations on, or near, manifolds

J Armstrong, T King - Proceedings of the Royal Society A, 2022 - royalsocietypublishing.org
Given a stochastic differential equation (SDE) in R n whose solution is constrained to lie in
some manifold M⊂ R n, we identify a class of numerical schemes for the SDE whose …

Drift-preserving numerical integrators for stochastic Poisson systems

D Cohen, G Vilmart - International Journal of Computer …, 2022 - Taylor & Francis
We perform a numerical analysis of a class of randomly perturbed Hamiltonian systems and
Poisson systems. For the considered additive noise perturbation of such systems, we show …

Splitting integrators for stochastic Lie–Poisson systems

CE Bréhier, D Cohen, T Jahnke - Mathematics of Computation, 2023 - ams.org
We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by
Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisson …

Structure-preserving numerical methods for stochastic Poisson systems

J Hong, J Ruan, L Sun, L Wang - arXiv preprint arXiv:2006.03880, 2020 - arxiv.org
We propose a class of numerical integration methods for stochastic Poisson systems (SPSs)
of arbitrary dimensions. Based on the Darboux-Lie theorem, we transform the SPSs to their …

An energy-conserving method for stochastic Maxwell equations with multiplicative noise

J Hong, L Ji, L Zhang, J Cai - Journal of Computational Physics, 2017 - Elsevier
In this paper, it is shown that three-dimensional stochastic Maxwell equations with
multiplicative noise are stochastic Hamiltonian partial differential equations possessing a …

Projection methods for stochastic differential equations with conserved quantities

W Zhou, L Zhang, J Hong, S Song - BIT Numerical Mathematics, 2016 - Springer
In this paper, we consider the numerical methods preserving single or multiple conserved
quantities, and these methods are able to reach high order of strong convergence …