Resonance based schemes for SPDEs

J Armstrong-Goodall, Y Bruned - arXiv preprint arXiv:2312.16690, 2023 - arxiv.org
Resonance based numerical schemes are those in which cancellations in the oscillatory
components of the equation are taken advantage of in order to reduce the regularity …

Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations

CE Bréhier, D Cohen, J Ulander - arXiv preprint arXiv:2302.08858, 2023 - arxiv.org
We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference
discretization in space for approximating the solutions to a class of nonlinear stochastic heat …

[HTML][HTML] Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

CE Bréhier, D Cohen - Applied Numerical Mathematics, 2023 - Elsevier
We analyze the qualitative properties and the order of convergence of a splitting scheme for
a class of nonlinear stochastic Schrödinger equations driven by additive noise. The class of …

Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations

CE Bréhier, D Cohen, G Giordano - arXiv preprint arXiv:2207.10484, 2022 - arxiv.org
We design and study splitting integrators for the temporal discretization of the stochastic
FitzHugh--Nagumo system. This system is a model for signal propagation in nerve cells …

An energy-conserving Fourier particle-in-cell method with asymptotic-preserving preconditioner for Vlasov-Ampère system with exact curl-free constraint

Z Li, Z Xu, Z Yang - Journal of Computational Physics, 2023 - Elsevier
We present an efficient and accurate energy-conserving implicit particle-in-cell (PIC)
algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness …

[PDF][PDF] Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

CE Bréhier, D Cohen, J Ulander - ESAIM: Mathematical Modelling …, 2024 - esaim-m2an.org
We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference
discretization in space for approximating the solutions to a class of semilinear stochastic …

Splitting integrators for linear Vlasov equations with stochastic perturbations

CE Bréhier, D Cohen - arXiv preprint arXiv:2402.18982, 2024 - arxiv.org
We consider a class of linear Vlasov partial differential equations driven by Wiener noise.
Different types of stochastic perturbations are treated: additive noise, multiplicative It\^ o and …

Exponential integrators for the stochastic Manakov equation

A Berg, D Cohen, G Dujardin - arXiv preprint arXiv:2005.04978, 2020 - arxiv.org
This article presents and analyses an exponential integrator for the stochastic Manakov
equation, a system arising in the study of pulse propagation in randomly birefringent optical …

Numerical Modeling of Stochastic Differential Problems with Applications

G Giordano - 2023 - elea.unisa.it
The interest in the study of stochastic differential equations has grown considerably in recent
years. The main reason for this interest is that stochastic differential equations are a potential …

Approximated exponential integrators for the stochastic Manakov equation

A Berg, D Cohen, G Dujardin - Journal of Computational Dynamics, 2023 - aimsciences.org
This article presents and analyzes an approximated exponential integrator for the
(inhomogeneous) stochastic Manakov system. This system of SPDE occurs in the study of …