Kinetic roughening in the nonlocal Kardar–Parisi–Zhang growth: Pseudospectral versus finite difference schemes

Abstract

To investigate the effects of nonlocal interaction in kinetic roughening, we adopt two independent numerical methods including pseudospectral (PS) and finite difference (FD) schemes to simulate the nonlocal Kardar–Parisi–Zhang (NKPZ) equation in (1+1)-dimensions. We find that the values of growth exponent β increase gradually with the spatial decay exponent ρ, indicating that the scaling properties are dependence on nonlocal interactions within the effective spatial decay region. However, our simulations also imply that both the local roughness exponent αloc and the spectral roughness exponent αs decrease slightly with ρ. Our results could be consistent with each other using these two numerical methods, and the comparisons and differences among the existing analytical predictions and numerical results are also discussed.