Wide-band, space-frequency approach is applied to simulations of a pulsed-driven free-electron laser (FEL), operating in THz regime. The model is based on the expansion of the total electromagnetic field (radiation and space-charge waves) in terms of transverse eigen-modes of the (cold) cavity, in which the field is excited and propagates. This approach has being successfully used for analysis of wide-band interactions in free-electron lasers operating in the linear and non-linear regimes. In a photo-cathode, RF-LINAC based FEL, ultra-short intense electron pulses can be obtained to production of a highly effective, super-radiant emission of a powerful coherent radiation at THz frequencies. Unfortunately, strong space-charge effects can be present in such configuration, restricting its applicability and requesting for a careful theoretical treatment. Direct application of the space-frequency formalism to description of space-charge fields was found ineffective. Lorenz-transformed 3D Coulomb field approximation is applied in the present work instead, enabling effective simulations of space-charge effects in free-electron devices.