Adaptive Numerics for Linear ODE Systems with Time-Dependent Data; Application in Photovoltaics

We give a brief account on the numerical approximation of linear evolution systems with time-dependent data. In particular, exponential integrators of Magnus type are considered. As an application we consider a system modeling the effect of photon impact of electrons in photovoltaic cells, in form of a time-dependent system of ordinary differential equations (ODEs) of spatially discrete Schrödinger type. Adaptive tuning of time steps in course of the numerical integration is an essential point; this is based on recently developed computable local error estimators. Numerical results are presented.