Von Neumann Stability Analysis of Finite Difference Schemes for Maxwell–Debye and Maxwell–Lorentz Equations

We address the stability study of finite difference schemes for Maxwell–Debye and Maxwell–Lorentz models. To this aim we selected the same schemes as those already studied by Petropoulos [6], who after having correctly defined characteristic polynomials associated to each scheme, merely computed its roots with a numerical algorithm. This implies having to specify values for the physical parameters which occur in the models as well for the time and space steps chosen for the discretization. The analysis has therefore to be carried out anew for each new material or discretization. We perform here a von Neumann analysis on the characteristic polynomials in their literal form, which yields once and for all stability conditions which are valid for all materials.