  Strongly interacting electrons in solids are generically described by
Hubbardtype models, and the impact of solar light can be modeled by an
additional time-dependence. This yields a finite dimensional system of ordinary
differential equations (ODE)s of Schr\"odinger type, which can be solved
numerically by exponential time integrators of Magnus type. The efficiency may
be enhanced by combining these with operator splittings. We will discuss
several different approaches of employing exponential-based methods in
conjunction with an adaptive Lanczos method for the evaluation of matrix
exponentials and compare their accuracy and efficiency. For each integrator, we
use defect-based local error estimators to enable adaptive time-stepping. This
serves to reliably control the approximation error and reduce the computational
effort
