Different methods for the numerical solution of a stochastic growth equation capturing the essence of amorphous thin film growth are presented and compared. We show numerically that the finite difference approximation and the spectral Galerkin method yield the same results within the same accuracy and roughly comparable computation time. We also explain how stochastic field equations can be solved using finite element approximations.

PACS numbers: 02.60.Cb, 02.60.Lj, 02.50.Ey, 68.55.--a