In this paper we model the streaming potential (SP) and the electroviscous effects (EVE) in a soft nanochannel for system parameters that forbid the use of linearized Debye-Huckel (DH) treatment. This linear treatment, which is an essential ingredient in electrokinetics modeling, necessitates that the system parameters must be such that the electrostatic potential in the entire system must be much smaller than k(B)T/ez (where k(B)T is the thermal energy, z is the ion valence and e is the electronic charge). In our previous paper we provided analytical results for the SP and the EVE in a soft nanochannel considering the DH treatment. Therefore, in this paper we extend this previous calculation; our numerical approach allows studying much wider ranges of parameters. This numerical treatment is based on solution of an integro-differential equation governing the flow velocity; to the best of our knowledge such an approach has never been previously used for SP modeling. In our previous study, we have witnessed an enhanced SP and an enhanced EVE for the soft nanochannel for the case of small electrostatic potential. Here our numerical results help us predict a breakdown of these trends for the case of larger potentials. These findings are important to probe the problem of SP and EVE in soft nanochannels across a sufficiently large range of electrostatic potentials, with implications in issues such as electrochemomechanical energy conversion. (C) 2015 Elsevier Inc. All rights reserved.