A pseudo-spectral method for the Kardar-Parisi-Zhang equation

Abstract

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.