论文标题
某些标量有限差异方案的稳定性理论：修改方程方法的有效性
Stability theory for some scalar finite difference schemes : Validity of the modified equations approach
论文作者
论文摘要
在本文中，我们讨论了修改方程方法的某些局限性，作为一类显式线性方案的稳定性分析工具，以标量偏导数方程。我们表明，通过修改方程的傅立叶变换获得的无限序列并不总是收敛的，并且在发散的情况下，它与方案无关。基于这些结果，我们解释了何时对修改方程的给定截断的稳定性分析可能会对相关方案的稳定性条件进行合理的估计。我们通过一些方案（即热方程式和传输方程）的方案的一些示例来说明我们的分析。
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by Fourier transform of the modified equation is not always convergent and that in the case of divergence, it becomes unrelated to the scheme. Based on these results, we explain when the stability analysis of a given truncation of a modified equation may yield a reasonable estimation of a stability condition for the associated scheme. We illustrate our analysis by some examples of schemes namely for the heat equation and the transport equation.
