This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same problem and used different tools to arrive at results that do not immediately coincide. We show the equivalence of the results as well as the equivalence of the approaches, unifying the two directions.

翻译：本文针对线性时变偏微分方程中全隐式龙格-库塔方法所产生矩阵的两类谱分析结果进行研究。这些结果源自同一问题的不同表述形式，并采用不同分析工具得出了初看并不直接吻合的结论。我们证明了这些结果的等价性以及分析方法的等效性，从而统一了这两个研究方向。