An explicit Milstein-type scheme for simulation of SDEs

In the present paper, we developed a new explicit Milstein-type integrator for stiff SDEs. Theoretically, we indicate that the scheme converges to the true value with a strong order of 1.0. For linear scalar SDE, the asymptotic mean square stability of our method is investigated. For all time steps, we prove that the presented integrator is asymptotically mean square stable. In addition, the A-stability and L-stability of the scheme was discussed in the mean square sense. For dimension two of the submitted scheme, the asymptotic mean square stability of two test systems has been analyzed. Numerical simulations confirm the theoretical results.