  We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang
equation in generic spatial dimensions. It is based on a momentum-space
discretization of the continuum equation and on a pseudo-spectral approximation
of the non-linear term. The method is tested in (1+1)- and (2+1)- dimensions,
where it is shown to reproduce the current most reliable estimates of the
critical exponents based on Restricted Solid-on-Solid simulations. In
particular it allows the computations of various correlation and structure
functions with high degree of numerical accuracy. Some deficiencies which are
common to all previously used finite-difference schemes are pointed out and the
usefulness of the present approach in this respect is discussed.
