Using Generalized Laguerre Polynomials to Compute the Matrix Exponential in Burnup Equations

Burnup calculations consider the time dependence of the material composition or isotope inventory, which has important influence on the neutronic properties of a nuclear reactor. An essential part of burnup calculations is to solve the burnup equations, which can be approximately treated as a first-order linear system and can be solved by means of matrix exponential methods. However, because of the large decay constants of short-lived nuclides, the coefficient matrix of the burnup equations has a large norm and a vast range of spectra. Consequently, it is quite difficult to directly compute the matrix exponential using conventional methods such as the truncated Taylor expansion and the Pade approximation. Recently, the Chebyshev rational approximation method (CRAM), which is based on rational functions on the complex plane, has shown the capability to deal with this problem. In this paper an alternative method based on the generalized Laguerre polynomials is proposed to compute the exponential of the burnup matrix. Against CRAM, the Laguerre polynomial approximation method (LPAM) has simple recursions for obtaining the coefficients in any order, and all the computations are real arithmetic. A point burnup case and a pin-cell burnup case are calculated for validation, and results show that LPAM is promising for burnup calculations.