In this paper, finite element method correlated with boundary conditions has been used to solve the Poisson’s equation. Splitting method, solving the continuity equation in two-time step, with and without term source associated with new Schottky injection application, however, Runge–Kutta method with a Gaussian filter calculated the distribution of all charges whether mobile or trapped accumulated on the interface. Moreover, these equations are solved in order to simulate the space charge behavior accumulated in the bi-dielectric system with different nature of electrodes. This model takes into account trapping, detrapping, recombination as well as the diffusion. Moreover, this model is optimized in order to fit experimental data by considering the surface charge at electrodes. Simulation results showed that the injection mechanism based on both the electric field and the properties of either metal-electrode or the dielectric. Furthermore, the polarity of the interfacial charge trapped on the dielectric interface depends on both the dielectrics permittivities and the nature of the electrodes. Thereby, surface charge at electrode improving the performance of this model to simulate the other charge accumulated into the bulk of the bi-dielectric system rather the interfacial charge trapped on the dielectric interface.