  We propose an alternative implementation of the Projected Gross-Pitaevskki
equation adapted for numerical modeling of the atomic Bose-Einstein condensate
trapped in a toroidally-shaped potential. We present an accurate and efficient
scheme to evaluate the required matrix elements and calculate time evolution of
the matter wave field. We analyze the stability and accuracy of the developed
method for equilibrium and nonequilibrium solutions in a ring-shaped trap with
additional barrier potential corresponding to recent experimental realizations.
