Analytical exponential model for stochastic point kinetics equations via eigenvalues and eigenvectors

Abstract

The stochastic point kinetics equations with a multi-group of delayed neutrons, which are the system of a couple of stiff stochastic differential equations, are presented. The analytical exponential model is used to solve the stochastic point kinetics equations in the dynamical system of the nuclear reactor. This method is based on the eigenvalues and corresponding eigenvectors of the coefficient matrix. The analytical exponential model calculates the mean and standard deviations of neutrons and precursor populations for the stochastic point kinetics equations with step, ramp, and sinusoidal reactivities. The results of the analytical exponential model are compared with published methods and the results of the deterministic point kinetics model. This comparison confirms that the analytical exponential model is an efficient method for solving stochastic stiff point kinetics equations.