Fundamental matrix method for the reactor kinetics equations of multi-group of delayed neutrons

Abstract

The point reactor kinetics equations of multi-group of delayed neutrons are a system of stiff ordinary differential equations. The fundamental matrix method is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix of the homogenous linear differential equations. The point reactor kinetics equations are rewritten in the matrix form of differential equations. The fundamental matrix of this system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the solution of this method is defined and discussed. The fundamental matrix method is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of the fundamental matrix method are compared with the results of the traditional methods. These comparisons substantiate the accuracy the fundamental matrix method.