  Recently, Donley et al. performed an experiment on the dynamics of collapsing
and exploding Bose-Einstein condensates by suddenly changing the scattering
length of atomic interaction to a large negative value on a preformed repulsive
condensate of $^{85}$Rb atoms in an axially symmetric trap. Consequently, the
condensate collapses and ejects atoms via explosions. We show that the accurate
numerical solution of the time-dependent Gross-Pitaevskii equation with axial
symmetry can explain some aspects of the dynamics of the collapsing condensate.
