This paper presents a numerical solution to the equations of point kinetics for nuclear power reactors, a set of seven coupled differential equations that describe the temporal variation of neutron density and the concentration of delayed neutron precursors. Due to the nature of the system, we propose to numerically solve the point kinetics equations by implementing the Adams-Bashforth and Adams-Moulton methods, which are predictor-corrector schemes with their respective modifiers to increase precision. The proposed method was tested computationally for different forms of reactivity with up to six groups of delayed neutron precursors. This method was used in a recent publication to solve the inverse problem of finding the reactivity. In this work, it is shown that it can also be used for the calculation of nuclear power, that it is simple and easy to implement, and that it produces good results when compared with those in the literature for neutron population density and concentration of delayed neutron precursors.