The influence of the neutron distribution governs the rate of the various reactions that occur within the nuclear reactor core, in addition to the stability of the reaction process in the fission chain. This work aims to characterize the neutron flux distribution into the nuclear reactor core as a function of one-dimensional space time-dependent for neutron telegraph two-energy groups system. An innovative onset using the finite difference method for the space–time dependent telegraph equations in the presence of two energy groups, multi-group of delayed neutrons, and time-varying reactivity has been developed. The system of neutron telegraph equations was rearranged based on adaptive matrix formation and numerical solution using theta method to obtain transient neutron distribution. Four cases of benchmark problems on one dimension are analyzed, which involve negative and positive perturbations in the thermal absorption, sinusoidal change in the thermal absorption, and instant change in the thermal fission.