Predictor-corrector pseudospectral methods for stochastic partial differential equations with additive white noise

Commonly used finite-difference numerical schemes show some deficiencies in the integration of certain types of stochastic partial differential equations with additive white noise. In this paper efficient predictor-corrector spectral schemes to integrate these equations are discussed. They are all based on the discretization of the system in Fourier space. The nonlinear terms are treated using a pseudospectral approach so as to speed up the computations without a significant loss of accuracy. The proposed schemes are applied to solve, both in one and two spatial dimensions, two paradigmatic continuum models arising in the context of nonequilibrium dynamics of growing interfaces: the Kardar-Parisi-Zhang and Lai-Das Sarma-Villain equations. Numerical results about the Lai-Das Sarma-Villain equation in two spatial dimensions have not been previously reported in the literature.