Matrix formulation for the calculation of nuclear reactivity

In this article, a new method for the calculation of nuclear reactivity using an equivalent matrix function for the concentration of delayed neutron precursors is presented for any given form of nuclear power. The matrix function can be written in a homogeneous system which is solved using an exponential matrix. Its solution requires to integrate the matrix function with respect to time, which originates a second matrix. The exponential form of the resulting matrix is calculated by analytical diagonalization, which reduces the computational cost by avoiding numerical calculation of the eigenvalues, eigenvectors or matrix inversion. The results of the nuclear reactivity calculations show a good precision of the proposed method for different time steps.