The main purpose of this paper is to perform a numerical analysis of the Neutron Spatial Kinetic Equations, subject to transients of the External Neutron Source, by applying the Implicit Euler Method as well as the Runge-Kutta Method in order to check which methods are best applicable in transients caused by External Neutron Source. For this purpose, a one-dimensional ADS reactor with a constant external source was simulated based on the geometry of ANL-BSS-6 reactor for benchmark effects.