Using Laguerre polynomials to compute the matrix exponential in burnup calculations

An essential part of burnup analysis is to solve the burnup equations. The burnup equations can be regarded as a first-order linear system and solved by means of matrix exponential methods. Because of its large spectrum, it is difficult to compute the exponential of the burnup matrix. Conventional methods of computing the matrix exponential, such as the truncated Taylor expansion and the Pade approximation, are not applicable to burnup calculations. Recently the Chebyshev Rational Approximation Method (CRAM) has been applied to solve burnup matrix exponential and shown to be robust and accurate. However, the main defect of CRAM is that its coefficients are not easy to obtain. In this paper, an orthogonal polynomial expansion method, called Laguerre Polynomial Approximation Method (LPAM), is proposed to compute the matrix exponential in burnup calculations. The polynomial sequence of LPAM can be easily computed in any order and thus LPAM is quite convenient to be utilized into burnup codes. Two typical test cases with the decay and cross-section data taken from the standard ORIGEN 2.1 libraries are calculated for validation, against the reference results provided by CRAM of 14 order. Numerical results show that, LPAM is sufficiently accurate for burnup calculations. The influences of the parameters on the convergence of LPAM are also discussed. (authors)