Previous work has introduced the stability analysis of coupled neutronics-depletion solvers for the standard explicit Euler and predictor-corrector methods. The present work is an extension of this analysis to higher-order schemes that are commonly used, including the LE, LE/LI, LE/QI, and their implicit versions where such a method exists. Substepping, extrapolation, and linear and quadratic interpolation are investigated, and their effects on numerical stability are discussed. A realistic, numerically-stiff depletion system is considered by applying automatic differentiation to the Chebyshev rational approximation method; accounting for initial nonlinear behaviour, the predictions from the stability analysis match the outcomes of simulation.

以前的工作介绍了标准显式 Euler 和预测器-校正器方法的耦合中子学耗竭求解器的稳定性分析。目前的工作是将此分析扩展到常用的高阶方案，包括 LE、LE/LI、LE/QI 及其存在此类方法的隐式版本。研究了子步法、外推法以及线性和二次插值法，并讨论了它们对数值稳定性的影响。通过对切比雪夫有理近似方法应用自动微分，考虑了一个现实的、数值刚性的耗尽系统；考虑到初始非线性行为，稳定性分析的预测与模拟结果相匹配。