Explicit Stochastic Runge-Kutta Methods with Large Stability Regions

Our aim is to derive explicit Runge‐Kutta schemes for Stratonovich stochastic differential equations with a multidimensional Wiener process, which are of weak order 2 and which have large stability regions. This has been achieved by the use of a technique in Chebyshev methods for ordinary differential equations. In this talk, large stability regions of our schemes will be shown. Concerning convergence order and stability properties, the schemes will be tested in numerical experiments.