  Convexity splitting like schemes with improved accuracy are proposed for a
phase field model for surface diffusion. The schemes are developed to enable
large scale simulations in three spatial dimensions describing experimentally
observed solid state dewetting phenomena. We introduce a first and a second
order unconditionally energy stable scheme and carefully elaborate the loss in
accuracy associated with large time steps in such schemes. We then present a
family of Rosenbrock convex splitting schemes. We show the existence of a
maximal numerical timestep and demonstrate the increase of this maximal
numerical time step by at least one order of magnitude using a Rosenbrock
method. This scheme is used to study the effect of contact angle on solid state
dewetting phenomena.
