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 …

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 …

As numerous modern challenges in scientific questions, industrial needs, and societal
requirements emerge, the demand for designing numerical methods to solve tremendously …

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 …

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 …

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 …

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 …

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 …

In this paper, it is shown that three-dimensional stochastic Maxwell equations with
multiplicative noise are stochastic Hamiltonian partial differential equations possessing a …

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 …