||We present a numerical scheme for the calculation of incompressible three-dimensional boundary layers (3DBL), designed to take advantage of the 3DBL model's overall hyperbolic nature, which is linked to the existence of wedge-shaped dependence and influence zones. The proposed scheme, explicit along the wall and implicit in the normal direction, allows large time steps, thus enabling fast convergence. In order to keep this partly implicit character, the control volumes for the mass and momentum balances are not staggered along the wall. This results in a lack of numerical viscosity, making the scheme unstable. The implementation of a numerical diffusion, suited to the local zone of influence, restores the stability of the boundary layer scheme while preserving second-order space accuracy. The purpose of this article is to present the analytical and numerical studies carried out to establish the scheme's accuracy and stability properties.