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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. [ABSTRACT FROM AUTHOR]

The coupled Maxwell and time-dependent Kohn-Sham equations are solved using the Riemann-Silberstein vectors to represent the electromagnetic fields. Momentum-space time propagation of the Riemann-Silberstein vectors are proposed and test calculations are presented to show the accuracy of the approach. [ABSTRACT FROM AUTHOR]

An accurate method for time propagation of the coupled Maxwell and time-dependent Kohn-Sham (TDKS) equation is presented. The new approach uses a simultaneous fourth-order Runge-Kutta-based propagation of the vector potential and the Kohn-Sham orbitals. The approach is compared to the conventional fourth-order Taylor propagation and predictor-corrector methods. The calculations show several computational and numerical advantages, including higher computational performance, greater stability, better accuracy, and faster convergence. [ABSTRACT FROM AUTHOR]