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This technical report yields detailed calculations of the paper [1] (B.Bid\'egaray-Fesquet, "Stability of FD-TD schemes for Maxwell-Debye andMaxwell-Lorentz equations", Technical report, LMC-IMAG, 2005) which have beenhowever automated since (seehttp://ljk.imag.fr/membres/Brigitte.Bidegaray/NAUtil/). It deals with thestability analysis of various finite difference schemes for Maxwell--Debye andMaxwell--Lorentz equations. This work gives a systematic and rigorouscontinuation to Petropoulos previous work [5] (P.G. Petropoulos.,"Stability andphase error analysis of FD-TD in dispersive dielectrics", IEEE Transactions onAntennas and Propagation, 42(1):62--69, 1994).

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