Two distinct aspects of linear media, namely, material dispersion and non-stationarity are usually misinterpreted. The dispersive nature of media is taken into account by applying time-domain filtering processes (such as the convolution process between electric field and electric susceptibility in Maxwell’s equations). This implies that the impulse response of a dispersive material is time-dependent, although the material itself might be stationary. However, unlike dispersive media, time-varying media are non-stationary in nature; hence, Fourier analysis is not a valid approach in this case and more elaborate procedure is required. In this article, we present how non-stationarity and dispersion are treated in time-domain numerical schemes. Moreover, we show the case when both aspects are present in one material, such as time-varying plasma. Numerical results are verified by comparisons with analytical solutions.