差分格式的余项效应分析及其应用

刘儒勋; 周朝晖

差分格式的余项效应分析及其应用

中国科学技术大学数学系

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出版历程
- 收稿日期: 1992-05-28
- 刊出日期: 1995-01-15

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

Dept. of Math., University of Sci. &Tech. of China, Hefei

摘要

摘要: 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Modified PDE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.
- 差分格式 /
- 余项效应 /
- 群速度
Abstract: 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 correction is made;Second,a new systematic analysis method-remaider-effect analysis(abbr.REAM) is proposed by means of the modified partial differential equations(abbr.MPDE) of finite difference schemes.The analysis is based on the synthetical study of the rational dispersion and dissipation relations of finite difference schemes.And the method clearly possesses constructivity.
- finite difference scheme /
- remainder effect /
- group velocity

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参考文献(16)

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