Error analyses and evaluation for solving burnup equations with MMPA method

•The mathematical error model of the MMPA method for solving burnup equations is proposed.•The coefficients of the MMPA method with different orders are given.•Guidelines for using the MMPA method are provided to avoid deterioration of accuracy and efficiency. The Mini-Max Polynomial Approximation (MMPA) is a new method to solve burnup equations, which has attracted much attention due to its advantages of good computational accuracy and efficiency. Understanding its error mechanism is significant for its application in practical burnup calculations. In this research, a mathematical model is proposed to clarify the error mechanism of the MMPA method for the burnup calculation. Then the coefficients of the MMPA method with different orders are given by the Remez algorithm. The errors of the MMPA method with different orders in burnup calculation are compared and analyzed, especially in single-step burnup calculation and infinite-step burnup calculation. Three cases are selected to verify the correctness of the mathematical error model, including fresh fuel burnup, depleted fuel burnup and decay calculation. The results show that when the order is greater than 36, the calculation accuracy of the MMPA method is less than the numerical noise of double precision calculation. As the order increases, the step length sensitivity of the MMPA method decreases. Finally, the computational accuracy and computational efficiency of the MMPA method with different orders are compared with those of the 16th order Chebyshev Rational Approximation Method (CRAM). The accuracy of the 16th order CRAM is between the 32nd and 36th order MMPA method. And the computation time of MMPA methods below order 76 is less than that of the 16th order CRAM. The theoretical analysis results of the mathematical error model are consistent with the numerical results. Then several best practices for solving burnup equations using the MMPA method are presented: (1) It is recommended to use the MMPA method with orders above 36 and below 76, whose accuracy and efficiency are better than 16th order CRAM in different degrees. (2) In multi-physics coupled computation which may require a strategy of large step length calculation, increasing the order of the MMPA method can not only improve the computational accuracy but also improve the computational efficiency.