关于多层差分格式稳定性的注记

在研究相应于抛物型方程,特别是双曲型方程初边值问题的多层差分格式的稳定性时,常用的方法之一是有限Fourier方法,其特点是应用时较灵活,可获得多种类型的稳定性不等式和相应的稳定性条件,但这些都强烈依赖于初始条件的离散化方式。在这篇短文中以波动方程的三层差分格式为例,说明如何正确地使用这种方法分析多层差分格式的稳定性。

A Note on the Stability of Multi-Level Difference Schemes

In this note we discuss how to use finite Fourier method correctly to analysis the stability of mult-level difference schemes. As an example, we have showed that the classical explicit scheme with usual initial data for the initial-boundary problem of wave equation is not stable when the mesh ratio r = l and have also showed that we can modify one of the initial data to get stability when r=1.