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A numerical code which calculating the spatio-temporal development of the discharge current in the Townsend regime has been developed. This code was written in Fortran 77. The individual contribution of electrons, positive, and negative ions to the total measurable current in the pulsed discharge is calculated by solving the corresponding set of coupled continuity equations for each species, for which boundary and initial conditions are set adequately. This simulation code is also capable of considering a more realistic scheme of photoelectron emission, such as that produced using a pulsed ultraviolet laser. In addition, the processes of ion and electron drift and longitudinal diffusion, electron detachment, negative-ion stabilization, and ion conversion have been calculated successfully. Some of these effects are extremely difficult to model analytically, and the simultaneous inclusion of two or more of them proves practically impossible. The power of this method in simulating complex discharge situations is discussed in this paper by means of examples considering the processes of electron and ion drift, diffusion, electron impact ionization and attachment, electron detachment, and negative-ion stabilization.