We present the exact computer simulation of transient space-charge limited transport under double injection in disorder materials. In this study, we focus on the phenomena related to the application of electro luminescence. We studied both the transport, i.e., charge carrier generation, their delocalized transport, trapping and detrapping, and the recombination currents, where we concentrated on the energy, time and spatial dependence of the recombination. In connection with the experiment, we modeled a situation after excess carriers generated by short pulses of a strongly absorbed light in a sandwich sample. An implicit (backward) Euler numerical method is utilized to obtain the transient solution of the nonlinear partial differential equations that describe charge carrier transport, trapping and recombination processes. We used amorphous hydrogenated silicon (a–Si:H) as an example material for the application of this method.