A Comparative Study of Ten Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations

Abstract

Point reactor neutron kinetics equations describe the time-dependent neutron density variation in a nuclear reactor core. These equations are widely applied to nuclear system numerical simulation and nuclear power plant operational control. This paper analyzes the characteristics of ten different basic or normal methods to solve the point reactor neutron kinetics equations. The accuracy after introducing different kinds of reactivity, stiffness of methods, and computational efficiency are analyzed. The calculation results show that: considering both the accuracy and stiffness, implicit Runge–Kutta method and Hermite method are more suitable for solution on these given conditions. The explicit Euler method is the fastest, while the power series method spends the most computational time.