1D model of an orificed hollow cathode using Matlab

I am a PhD student in aerospace engineering and I need help implementing a 1D plasma model of an orificed hollow cathode in Matlab. The model is described in: ‘One-Dimensional Hollow Cathode Model’ by Katz et al. I tried it myself but could not obtain results and I have difficulties understanding some details of the model. The paper, explanations of my approach as well as my matlab script are attached.