Abstract In this paper, the generalisation of the 4th-order Adams-Bashforth-Moulton predictor-corrector method is proposed to numerically solve the point kinetic equations of the nuclear reactivity calculations without using the nuclear power history. Due to the nature of the point kinetic equations, different predictor modifiers are used in order improve the precision of the approximations obtained. The results obtained with the prediction formulas and generalised corrections improve the precision when compared with previous methods and are valid for various forms of nuclear power and different time steps.