A numerical approach based on Haar wavelet operational method to solve neutron point kinetics equation involving imposed reactivity insertions

Abstract

The numerical solution of point kinetics equation with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. The continuous indication of the neutron density and its rate of change are important for the safe startup and operation of reactors. The Haar wavelet operational method (HWOM) is proposed to obtain the numerical approximate solution of neutron point kinetic equation appeared in nuclear reactor with time-dependent and independent reactivity function. The present method has been applied to solve stiff point kinetics equations elegantly with step, ramp, zig-zag and sinusoidal reactivity insertions. This numerical method has turned out as an accurate computational technique for many applications. The accuracy of the obtained solutions are quite high even if the number of collocation points is small. By increasing the number of collocation points, the error of the approximation solution rapidly decreases. In a systematic comparison with other existing methods, it may be concluded that the present method is simple and efficient.This method is applied to different types of reactivity in order to check the validity of the proposed method. Moreover, the obtained approximate results have been also compared with other available numerical results. It manifests that the results obtained by the HWOM are in good agreement with other available results even for large time range and it is certainly simpler than other methods in open literature.