content_image/353521.jpg
<img src='content_image/353521.jpg'>

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. 

