  We present a numerical study of the time-dependent and time-independent
Gross-Pitaevskii (GP) equation in two space dimensions, which describes the
Bose-Einstein condensate of trapped bosons at ultralow temperature with both
attractive and repulsive interatomic interactions. Both time-dependent and
time-independent GP equations are used to study the stationary problems. In
addition the time-dependent approach is used to study some evolution problems
of the condensate. Specifically, we study the evolution problem where the trap
energy is suddenly changed in a stable preformed condensate. In this case the
system oscillates with increasing amplitude and does not remain limited between
two stable configurations. Good convergence is obtained in all cases studied.
