71 citations · 176 across the 14 of their papers we have counts for
6 papers · 1 filter
Machine Learning Methods for Autonomous Ordinary Differential Equations
Maxime Bouchereau, Philippe Chartier, Mohammed Lemou +1
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even thou…
Uniformly accurate schemes for drift--oscillatory stochastic differential equations
Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou +1
In this work, we adapt the {\em micro-macro} methodology to stochastic differential equations for the purpose of numerically solving oscillatory evolution equations. The models we…
Averaging of highly-oscillatory transport equations
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent…
Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
Mohammed Lemou, Florian Méhats, Xiaofei Zhao
We apply the two-scale formulation approach to propose uniformly accurate (UA) schemes for solving the nonlinear Dirac equation in the nonrelativistic limit regime. The nonlinear D…
Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties
Philippe Chartier, Norbert J. Mauser, Florian Méhats +1
In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations.…
A boundary matching micro/macro decomposition for kinetic equations
Mohammed Lemou, Florian Méhats
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distributio…