Exponential integrators are a well-known class of time integration methods
that have been the subject of many studies and developments in the past two
decades. Surprisingly, there have been limited efforts to analyze their
stability and efficiency on non-diffusive equations to date. In this paper we
apply linear stability analysis to showcase the poor stability properties of
exponential integrators on non-diffusive problems. We then propose a simple
repartitioning approach that stabilizes the integrators and enables the
efficient solution of stiff, non-diffusive equations. To validate the
effectiveness of our approach, we perform several numerical experiments that
compare partitioned exponential integrators to unmodified ones. We also compare
repartitioning to the well-known approach of adding hyperviscosity to the
equation right-hand-side. Overall, we find that the repartitioning restores
convergence at large timesteps and, unlike hyperviscosity, it does not require
the use of high-order spatial derivatives.