Numerical stability for linear dispersive media via computer algebra
Résumé
The linear stability analysis of Finite Difference-Time Difference schemes can be reduced via von Neumann analysis to the study of a sequence of polynomials with coefficients depending on the physical parameters of the medium and the numerical parameters. A Computer Algebra environment has been designed to automize such calculations and is demonstrated on schemes for Maxwell-Debye and Maxwell-Lorentz systems. The possible generalization to other schemes and other applications will be emphasized.