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

TL;DR

This paper provides a detailed, systematic von Neumann stability analysis of finite difference schemes applied to Maxwell--Debye and Maxwell--Lorentz equations, extending previous work with rigorous calculations and automation.

Contribution

It offers a comprehensive and automated stability analysis framework for finite difference schemes in dispersive electromagnetic media, building on prior theoretical foundations.

Findings

Stability conditions for various finite difference schemes derived

Analysis extends to Maxwell--Debye and Maxwell--Lorentz models

Provides a systematic approach to stability verification

Abstract

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