  We study certain stationary and time-evolution problems of trapped
Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii
equation with both spherical and axial symmetries. We consider time-evolution
problems initiated by changing the interatomic scattering length or harmonic
trapping potential suddenly in a stationary condensate. These changes introduce
oscillations in the condensate which are studied in detail. We use a time
iterative split-step method for the solution of the time-dependent
Gross-Pitaevskii equation, where all nonlinear and linear nonderivative terms
are treated separately from the time propagation with the kinetic energy terms.
Even for an arbitrarily strong nonlinear term this leads to extremely accurate
and stable results after millions of time iterations of the original equation.
