  We extend the Projected Gross Pitaevskii equation formalism of Davis et al.
[Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case
of harmonic potentials. We outline a robust and accurate numerical scheme that
can efficiently simulate this system. We apply this method to investigate the
equilibrium properties of a harmonically trapped three-dimensional Bose gas at
finite temperature, and consider the dependence of condensate fraction,
position and momentum distributions, and density fluctuations on temperature.
We apply the scheme to simulate an evaporative cooling process in which the
preferential removal of high energy particles leads to the growth of a
Bose-Einstein condensate. We show that a condensate fraction can be inferred
during the dynamics even in this non-equilibrium situation.
