Time Discretizations for Maxwell-Bloch Equations

Brigitte Bidégaray (1, 2)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 LMC - IMAG - Laboratoire de Modélisation et Calcul

In this article we derive new time discretizations for the numerical simulation of Maxwell-Bloch equations. These discretizations decouple the equations, thus leading to improved efficiency. This approach may be combined with the fulfilment of physical properties, such as positiveness properties, which are not accounted for by classical schemes. Our time discretizations are moreover proved to be nonlinearly stable.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Brigitte Bidégaray. Time Discretizations for Maxwell-Bloch Equations. Numerical Methods for Partial Differential Equations, 2003, 19 (3), pp.284-300. ⟨10.1002/num.10046⟩. ⟨hal-00319990⟩