[en] A generalized Green's function technique for wave propagation of transient fields in one-dimensional media is developed. The medium is partitioned into an arbitrary number of subslabs for which Green operators that map the incident field to the internal fields are defined. Relations between the Green operators for the entire medium and the Green operators for the subslabs are derived. The technique leads to fast numerical algorithms that are especially efficient for dispersive media. The numerical examples focus on the comparison between wave propagation in dispersive and nondispersive media. 16 refs., 12 figs