关于数值振荡与数值稳定性关系的注记

Pieter Wesseling在其《计算流体力学原理》中构造了一个虽有数值振荡但却稳定的例子,研究上述例子,发现其结论有待修正.本文从直接解离散方程组和利用特征值理论两个方面,并作误差估计,都得出结论带有数值振荡的格式是不稳定的.

Remark About Numerical Wiggle and Numerical Stability

In the book of Principles of Computational Fluid Dynamics,Pieter Wesseling constructed an example which had wiggles but was stable.In this paper,we studied this example and found that there was something wrong in its conclusion,From two aspects,solution of discreted equation system and theory of eignvalue,and error estimation,we got the conclusion that the scheme with the wiggles was not stable.