The point reactor kinetics model with two energy groups for neutron population consists in a stiff system of linear/nonlinear ordinary differential equations. To solve the equations describing the system dynamics, we use the Theta method. Here, the one delayed neutron precursor approximation is considered into the matrix system of the point reactor kinetics model. Several numerical experiments with different reactivities and time steps are considered. Our results suggest that the related Theta method can be a useful tool to explore in depth reactor kinetics, offering enhanced efficiency in the computer time as compared to other methodologies. Comparisons with published methods are presented and discussed.