  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, etc. 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 mean-square sense, which answers an open problem in [Chen and Hong, SIAM J.
Numer. Anal., 2016] for stochastic Maxwell equations driven by additive noise.

Numerical Analysis