Linear mean-square stability analysis of weak order 2.0 semi-implicit Taylor schemes for scalar stochastic differential equations

As in the deterministic case, the introduction of implicitness in stochastic schemes improves the stability behavior. In this paper a complete study for the linear MS-stability of the two-parameter family of semi-implicit weak order 2.0 Taylor schemes for scalar stochastic differential equations is given. Figures of the MS-stability regions and numerical examples that confirm the theoretical results are shown.