  We conduct Smoothed Particle Hydrodynamics simulations of the `collect and
collapse' scenario (Elmegreen and Lada, 1977) for star formation triggered by
an expanding HII region. We simulate the evolution of a spherical uniform
molecular cloud with an ionising source at its centre. The gas in the cloud is
self-gravitating, although the cloud is prevented from globally collapsing. We
find that the shell driven by the HII region fragments to form numerous
self--gravitating objects. We repeat our calculations at four numerical
resolutions to ensure that they are converged. We compare our results to the
analytical model of Whitworth et al, 1994 and show that our simulations and the
predictions of Whitworth et al are in good agreement in the sense that the
shell fragments at the time and radius predicted by Whitworth et al to within
20% and 25% respectively. Most of the fragments produced in our two highest
resolution calculations are approximately half the mass of those predicted, but
this conclusion is robust against both numerical resolution and the presence of
random noise (local fluctuations in density of a factor of $\sim2$) in the
initial gas distribution. We conclude that such noise has little impact on the
fragmentation process.
