5 papers
Explicit domain preserving numerical schemes for a class of stochastic differential equations
Charles-Edouard Bréhier, David Cohen
We construct and analyze numerical schemes for systems of stochastic differential equations, which preserve almost surely a given hypercube of arbitrary dimension. We propose a new…
Analysis of a first-order explicit positivity preserving scheme for a class of scalar SDEs
Charles-Edouard Bréhier, David Cohen
We propose and analyze a first-order numerical scheme for a class of scalar Itô stochastic differential equations with almost surely positive solutions. We construct a new explicit…
General non-linear fragmentation with discontinuous Galerkin methods
Maxime Lombart, Charles-Edouard Bréhier, Mark Hutchison +1
Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain popula…
Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: applications to fluid turbulence and generation of fractional Gaussian fields
Geoffrey Beck, Charles-Edouard Bréhier, Laurent Chevillard +2
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has bee…
Splitting integrators for linear Vlasov equations with stochastic perturbations
Charles-Edouard Bréhier, David Cohen
We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative…