  Parareal is a widely studied parallel-in-time method that can achieve
meaningful speedup on certain problems. However, it is well known that the
method typically performs poorly on non-diffusive equations. This paper
analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods
on non-diffusive equations. By combining standard linear stability analysis
with a simple convergence analysis, we find that certain Parareal
configurations can achieve parallel speedup on non-diffusive equations. These
stable configurations all posses low iteration counts, large block sizes, and a
large number of processors. Numerical examples using the nonlinear Schrodinger
equation demonstrate the analytical conclusions.
