We consider the problem of approximating mild solutions of stochastic evolution equations in the mean-square sense. Therefore, an infinite dimensional version of a Runge-Kutta type scheme for the time discretization is proposed. The introduced scheme can be applied to a certain class of semilinear stochastic partial differential equations (SPDEs) with commutative as well as non-commutative noise. In case of non-commutative noise, iterated stochastic integrals of the driving Q-Wiener process have to approximated. Finally, the order of convergence and the efficiency of the new scheme will be discussed.

This is joint work with Claudine von Hallern (Universität Hamburg)