A comjDutational time-dependent study of the bistability in resonant tunneling structures including the electron-electron interactions is presented. A new computational method for the investigation of many jDarticle interacting systems for the study of quantum transport in small systems is introduced. The timedependence of the wave-function in the Schrödinger equation is studied by discretizing the energy spectrum and the time steps. A simple model for a double barrier resonant tunneling structure is introduced. The method is then applied to this simple model of double barrier resonant tunneling structure, and this geometry is investigated systematically in terms of inter-pcirticle interaction strength and number of particles. By applying the method to this simple geometry it is shown that there exists instabilities which occur a.s oscillcitions in the current-voltage characteristics of the model geometry.