Numerical solution of a continuum equation for interface growth in 2+1 dimensions

We present the results of extensive large-scale numerical integrations of the Kardar-Parisi-Zhang equation for stochastic interface growth in 1+1 and 2+1 dimensions as a function of the nonlinearity parameter {ε}. We find results for the growth exponents {α} and {β} close to those obtained for discrete models. In particular, we find that for large values of {ε}, the values of the exponents are close to the conjecture of Kim and Kosterlitz, indicating that the smaller values obtained previously are due to crossover effects. In contrast to recent studies of discrete models, our results do not show evidence of a phase transition in 2+1 dimensions for {ε}{≥}1.