RUNGE-KUTTA SEMIDISCRETIZATIONS FOR STOCHASTIC MAXWELL EQUATIONS WITH ADDITIVE NOISE

摘要

The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by additive noise. We show that the equations admit physical properties and mathematical structures, including regularity, energy and divergence evolution laws, and stochastic symplecticity. In order to inherit the intrinsic properties of the original system, we introduce a general class of stochastic Runge-Kutta methods and deduce the condition of symplecticity-preserving. By utilizing a priori estimates on numerical approximations and semigroup approach, we show that the methods, which are algebraically stable and coercive, are well-posed and convergent with order one in a mean-square sense, which answers an open problem in Remark 18 in [C. Chen and J. Hong, SIAM J. Numer. Anal., 54 (2016), pp. 2569-2593] for stochastic Maxwell equations driven by additive noise.