“…Especially Runge-Kutta (RK) methods are widely used. In the last decade, it has been widely recognized that the stochastic RK methods play an important role in numerically solving stochastic ODEs and popularly employed, see, e.g., [1,2,12,17,19,20,22,23,24] and the references therein. The symplectic condition of stochastic RK methods for stochastic Hamiltonian ODEs was obtained firstly in [19].…”