  We present the results of numerical time evolutions of the linearised
perturbations of rapidly and rigidly rotating Newtonian polytropes while making
the Cowling approximation. The evolution code runs stably for hundreds of
stellar rotations, allowing us to compare our results with previously published
eigenmode calculations, for instance the f-mode calculations of Ipser &
Lindblom, and the r-mode calculations of Karino et al. The mode frequencies
were found to be in agreement within the expected accuracy. We have also
examined the inertial modes recently computed by Lockitch & Friedman, and we
were able to extend their slow-rotation results into the rapid rotation regime.
In the longer term, this code will provide a platform for studying a number of
poorly understood problems in stellar oscillation theory, such as the effect of
differential rotation and gravitational radiation reaction on normal mode
oscillations and, with suitable modifications, mode-mode coupling in the mildly
non-linear regime.
