We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications include in particular highly-oscillatory Kubo oscillators and spatial discretizations of the nonlinear Schrödinger equation with fast white noise dispersion. We construct a method of weak order two with computational cost and accuracy both independent of the stiffness of the oscillations. A geometric modification that conserves exactly quadratic invariants is also presented.
A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems
An exponential integrator for a highly oscillatory Vlasov equation
Université Européenne de Bretagne, LMBA (UMR CNRS 6205), Université de Bretagne-Sud（欧洲布列塔尼大学，LMBA（CNRS联合研究单位6205），南布列塔尼大学）；Inria Nancy-Grand Est, CALVI Project & IRMA (UMR CNRS 7501), Université de Strasbourg（法国国家信息与自动化研究所南斯特拉斯堡分部，CALVI项目，IRMA（CNRS联合研究单位7501），斯特拉斯堡大学）；Max Planck Institute for Plasma Physics, EURATOM Association（马克斯·普朗克等离子体物理研究所，EURATOM协会）
Improved uniform error bounds of exponential wave integrator method for long-time dynamics of the space fractional Klein-Gordon equation with weak nonlinearity
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；University of Maryland（马里兰大学）
A Uniformly Accurate Multiscale Time Integrator for the Klein-Gordon-Schrödinger Equations in the Nonrelativistic Regime via Simplified Transmission Conditions
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Purdue University（普渡大学）；Université de Lorraine（洛林大学）；Inria Nancy-Grand Est（南锡大东部国家研究学院）
Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation
National Center for Applied Mathematics（应用数学国家研究中心）；Tianjin University（天津大学）；School of Mechanical and Aerospace Engineering, Jilin University（吉林大学机械与航空航天工程学院）；Jilin University（吉林大学）
