Optimal ϑ -Methods for Mean-Square Dissipative Stochastic Differential Equations

In this paper, we address our investigation to the numerical integration of nonlinear stochastic differential equations exhibiting a mean-square contractive character along the exact dynamics. We specifically focus on the conservation of this qualitative feature along the discretized dynamics originated by applying stochastic ϑ -methods. Retaining the mean-square contractivity under time discretization is translated into a proper stepsize restriction. Here we analyze the choice of the optimal parameter ϑ making this restriction less demanding and, at the same time, maximizing the stability interval. A numerical evidence is provided to confirm our theoretical results.