差分格式的余项效应分析及其应用

The REmainder-Effect Analysis of Finite Differencee Schemes and the Applications

本文对已有的差分格式的色散关系和群速度效应的Ｆｏｕｒｉｅｒ分析提出了置疑，指出症结所在，并予以纠正；并且利用差分格式的ＭｏｄｉｆｉｅｄＰＤＥ思想，提出了一种新的构造性差分格式分析方法——差分格式余项效应分析．这种方法基于差分格式的耗散关系和色散关系的综合分析．方法具有明显的构造性和现实意义．

In the present paper two contents are enclosed.First. the Fourier analysis approach of the dispersion relation and group velocity effect of finite difference schemes is discussed the defects of the approach is pointed out and the correctionis made.Second, a new systematic analysis nethod-remalder-effect analysis (abbr. REAM) is proposed by means of the modified partial differential equa-tions (abbr. MPDE) of finite difference schemes. The analysis is based on the synthetical stl1dy of the rational dispersion and the dissipation relations of finite difference scheme. And the method clearly possesses constructivity.