  The pseudo-spectral method is proposed for following the evolution of density
and velocity fluctuations at the weakly non-linear stage in the expanding
universe with a good accuracy. In this method, the evolution of density and
velocity fluctuations is integrated in the Fourier Space with using FFT. This
method is very useful to investigate accurately the non-linear dynamics in the
weakly non-linear regime. Because the pseudo-spectral method works directly in
the Fourier space, it should be especially useful for examining behavior in the
Fourier domain, for an example, the effects of the non-linear coupling of
different wave modes on the evolution of the power spectrum. I show the results
of this analysis both in one and three dimensional systems.
