Abstract <p>The article is devoted to the development and testing of projective difference schemes for modeling the components of an electromagnetic field in two-dimensional media. The difference schemes proposed are based on the projective version of the integral-interpolation method. Various formulations of boundary condition are proposed, and an algorithm for solving the Dirichlet boundary value problem using projective difference schemes is discussed. For comparison, the paper also considers a solution of the problem using difference schemes constructed by the central-difference approximation method. Numerical experiments were performed for a problem with known analytical expressions for the exact solution.</p>