Nonlinear resonant structures consisting of coupled ring resonators can be modeled by difference-differential equations that take into account non-instantaneous Kerr response and the effect of loss. We present a simple and efficient numerical formalism for solution of the system and calculation of the time evolution. The technique is demonstrated by investigating the dynamical behavior of the coupled structure with two rings, namely, focusing on self-pulsing solutions. The influence of both, loss and non-instantaneous Kerr response, is also presented.