A novel solver which uses finite wave averaging to mitigate oscillatory stiffness is proposed and
analysed. We have found that triad resonances contribute to the oscillatory stiffness of the problem and
that they provide a natural way of understanding stability limits and the role averaging has on reducing
stiffness. In particular, an explicit formulation of the nonlinearity gives rise to a stiffness regulator function
which allows for analysis of the wave averaging.
A practical application of such a solver is also presented. As this method provides large timesteps at
comparable computational cost but with some additional error when compared to a full solution, it is a
natural choice for the coarse solver in a Parareal-style parallel-in-time method
