This article presents a scheme for a semi-classical model of electromagnetic wave propagation in a non-centro-symmetric crystal of KDP. The model was throughfully described in [A Maxwell–Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP (submitted)]. It uses Maxwell's equations to describe the wave field and Bloch's equations for the medium at the quantum-mechanical level. We extend the Yee [Computational Electrodynamics: The Finite-difference Time-domain Method, second ed., Artech House, Boston, MA, 2000; IEEE Trans. Antennas Propag. AP-14 (1966) 302] scheme, in the undimensional case, used for isotropic media to treat the case of a KDP crystal, while ensuring an accurate scheme. Finally, several numerical simulations are performed.