Two-dimensional (2D) materials attract a lot of interest for the development of novel nanoelectronic devices, owing to their monolayer nature, which allows for integration in planar devices. The most well-known example of such a material is graphene. Another class of 2D materials are transition metal dichalcogenides (TMDCs), which exhibit similar properties as graphene (superior carrier mobility, high cut-off frequency, etc), but are still distinct. From an electronic viewpoint, TMDCs range from being metallic to semiconducting. Moreover, these materials display strong spin-orbit-induced band splitting and spin-valley coupling, making them candidates for spintronic and valleytronic devices. The overall goal of the proposed project is to model this new class of 2D materials, following a four-step approach. First, as the charge carriers in TMDCs behave as Dirac particles, novel nonuniform and higher-order finite-difference time-domain (FDTD) schemes for the Dirac equation will be developed. Second, hybrid implicit-explicit FDTD schemes for Maxwell’s equations, allowing for the inclusion of 2D materials, will be investigated. Third, the Maxwell-Dirac system for general 2D materials will be studied, with focus on accuracy and efficiency of the numerical algorithms. Fourth, the FDTD-based numerical schemes will be applied to TMDC-based devices, as such demonstrating their potential to support the design of electronic, spintronic, and valleytronic circuits.