Abstract The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. We show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

中文翻译：

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Chebyshev有理逼近法的全局误差分析

摘要 切比雪夫有理逼近法（CRAM）已成为解决核耗竭问题的广泛采用的方法。因此，了解CRAM的准确性对于核电站的安全运行具有重要意义。本文对 CRAM 进行了全局误差分析，发现随着时间步长接近零，在固定结束时间测量的精确解和 CRAM 解之间的相对误差对于偶数阶和奇数阶分别接近 1 和无穷大；对于中间时间步长，观察到最小的相对误差。我们表明 CRAM 行为的原因是方法不一致。从这些结果得出的使用 CRAM 的两个最佳实践是：(1) 使用 CRAM 阶数 16 或更高，(2) 如有必要，当多物理场耦合需要较小的时间步长时，增加 CRAM 阶数。