Related papers: Casimir preserving stochastic Lie-Poisson integrat…
We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics…
Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable…
We introduce energy-preserving integrators for nonholonomic mechanical systems. We will see that the nonholonomic dynamics is completely determined by a triple $({\mathcal D}^*, \Pi, \mathcal{H})$, where ${\mathcal D}^*$ is the dual of the…
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic L\'evy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
The numerical integration of the Benjamin and Benjamin--Ono equations are considered. They are non-local partial differential equations involving the Hilbert transform, and due to this, so far quite few structure-preserving integrators have…
In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley (2009) and Schubert et al. (2009), possesses a rich…
We develop new numerical schemes for Vlasov--Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is…
We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary…
Numerical methods that approximate the solution of the Vlasov-Poisson equation by a low-rank representation have been considered recently. These methods can be extremely effective from a computational point of view, but contrary to most…
In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow…
We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved…
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension we numerically simulate singular solutions (peakons)…
The Langevin equation with a multiplicative L\'evy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed.…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…
In this paper, we present an energy-preserving exponentially integrable numerical method for stochastic wave equation with cubic nonlinearity and additive noise. We first apply the spectral Galerkin method to discretizing the original…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
Nonlinear random vibration under excitations of both Gaussian and Poisson white noises is considered. The model is based on stochastic differential equations, and the corresponding stochastic integrals are defined in such a way that the…
This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame…