  The integrating factor and exponential time differencing methods are
implemented and tested for solving the time-dependent Kohn--Sham equations.
Popular time propagation methods used in physics, as well as other robust
numerical approaches, are compared to these exponential integrator methods in
order to judge the relative merit of the computational schemes. We determine an
improvement in accuracy of multiple orders of magnitude when describing
dynamics driven primarily by a nonlinear potential. For cases of dynamics
driven by a time-dependent external potential, the accuracy of the exponential
integrator methods are less enhanced but still match or outperform the best of
the conventional methods tested.
