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We consider the discretization in time of a system of parabolic stochasticpartial differential equations with slow and fast components; the fast equationis driven by an additive space-time white noise. The numerical method isinspired by the Averaging Principle satisfied by this system, and fits to theframework of Heterogeneous Multiscale Methods.The slow and the fast componentsare approximated with two coupled numerical semi-implicit Euler schemesdepending on two different timestep sizes. We derive bounds of theapproximation error on the slow component in the strong sense - approximationof trajectories - and in the weak sense - approximation of the laws. Theestimates generalize the results of \cite{E-L-V} in the case of infinitedimensional processes.

Analysis of a HMM time-discretization scheme for a system of Stochastic PDE's