Pseudospectral method for the Kardar-Parisi-Zhang equation

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 pseudospectral approximation of the nonlinear term. The method is tested in $\mathrm{}(1+1)\mathrm{}$ and $\mathrm{}(2+1)\mathrm{}$ 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 that are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.