10 0 10 2 10 4 t 10 -1 10 0 w(t) 10 -3 10 -2 10 -1 10 0 k 10 -2 10 0 10 2 10 4 S(k) FIG. 1: Numerical results for the global width and structure factor ( inset ) averaged over 100 runs in a system of size L = 1024 with λ = 4. We employ the different discretization schemes indicated in Eqs. (47), (48) and (30,31) (from bottom to top). Curves are slightly shifted vertically for clarity. Lines are plotted as a guide with exponent β$_{KPZ}$ = 0 . 3 ( dashed ), β = 0 . 25 ( dot-dashed ), and − 2 ( solid, in the inset ). All discretization schemes are consistent with the KPZ scaling. where ̂ h$_{k}$ ( t ) is as before (see Sec. IV) the Fourier transform of the interface profile. According to the previous scaling Ansatz, S ( k, t ) scales as k − (2 α +1) with the roughness exponent α . We observe that all the discretization schemes are consistent with the KPZ scaling, with the KPZ exponents α = 1 / 2 and β = 1 / 3. It can also be observed from Fig. 1 that the crossover from the transient linear (Edwards–Wilkinson) behavior to the asymptotic nonlinear (KPZ) behavior appears earlier in both alternative discretization schemes than in the standard one [Eq. (47)]. This effect is presumably related to the fact that the nonlinearity of the alternative schemes always makes a much stronger contribution to the dynamics than the one in the standard scheme, see Fig. 2 below. This way, the threshold contribution from the nonlinearity is received sooner, resulting in an anticipated departure from the transient linear regime. 18