  We consider the numerical integration of the Gross-Pitaevskii equation with a
potential trap given by a time-dependent harmonic potential or a small
perturbation thereof. Splitting methods are frequently used with Fourier
techniques since the system can be split into the kinetic and remaining part,
and each part can be solved efficiently using Fast Fourier Transforms. To split
the system into the quantum harmonic oscillator problem and the remaining part
allows to get higher accuracies in many cases, but it requires to change
between Hermite basis functions and the coordinate space, and this is not
efficient for time-dependent frequencies or strong nonlinearities. We show how
to build new methods which combine the advantages of using Fourier methods
while solving the timedependent harmonic oscillator exactly (or with a high
accuracy by using a Magnus integrator and an appropriate decomposition).
