A simple approach is extended for the simulation of Kerr-nonlinear and/or dispersive media through the finite-difference time-domain method. The scheme is able to include different types of linear and nonlinear dispersion in a single and unified formulation. It also provides a method for the simulation of nonlinear dispersive media in such a way that saving time is possible. Also, a new simple technique is presented for the implementation of sources having arbitrary profiles and arbitrary radiation angles. The technique is particularly suited for easy modeling of unidirectional sources like Gaussian beams.