  Three pseudospectral algorithms are described (Euler, leapfrog and trapez)
for solving numerically the time dependent nonlinear Schroedinger equation in
one, two or three dimensions. Numerical stability regions in the parameter
space are determined for the cubic nonlinearity, which can be easily extended
to other nonlinearities. For the first two algorithms, maximal timesteps for
stability are calculated in terms of the maximal Fourier harmonics admitted by
the spectral method used to calculate space derivatives. The formulas are
directly applicable if the discrete Fourier transform is used, i.e. for
periodic boundary conditions. These formulas were used in the relevant
numerical programs developed in our group.
