Time Discretizations for Maxwell-Bloch Equations

Self Induced Transparency. Comparison of splitting schemes.


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.

Mathematical Models and Methods in Applied Sciences, 19(3), 284–300 (2003)