The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations (Q732414)

Using certain methods of the form \[ \begin{aligned} y_{n+1} & =y_{n}+A^{(i)}(t_{n},y_{n},y_{n+1},h,\Delta W_{n}),\;i=1,2,\\ t_{n} & =t_{0}+nh,\;\Delta W_{n}=W(t_{n+1})-W(t_{n}), \end{aligned} \] for a numerical solution of Stratonovich stochastic differential equations, the authors produce a composite method \[ y_{n+1}=y_{n}+\lambda_{n}A^{(1)}+(1-\lambda_{n})A^{(2)}, \] where \(\lambda_{n}\) depends on \(t_{n}\), \(y_{n}\), \(y_{n+1}\), \(h\), \(\Delta W_{n}.\) They construct two specific composite methods and study their convergence and stability properties.