The comparison of the various techniques introduced in the literature together with a new scheme reported here have been applied to the study of a nonlinear directional coupler made of two identical buried guides of non-linear kerr-type materials. A new stable and accurate marching finite-element scheme based on the split-operator technique, is described for the scalar propagation analysis of optical waveguides with arbitrary cross-section and inhomogeneous nonlinear dielectrics. In this method, to keep the scheme explicit, the refraction contribution is computed by its corresponding taylor expansion. Extensive numerical experiments have shown that the number of terms in the taylor expansion is important to ensure global accuracy and stability for the present approach.