| 差分格式的余项效应分析及其应用 |
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| 引用本文： | 刘儒勋,周朝晖.差分格式的余项效应分析及其应用[J].应用数学和力学,1995,16(1):80-90. |
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| 作者姓名： | 刘儒勋 周朝晖 |
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| 作者单位： | 中国科学技术大学数学系 |
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| 摘 要： | 本文对已有的差分格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，人有明显的构造性和现实意义。
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| 关 键 词： | 差分格式 余项效应 微分方程 数值解 |
The REmainder-Effect Analysis of Finite Differencee Schemes and the Applications |
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| Liu Ru-xun Zhou Zhao-hui.The REmainder-Effect Analysis of Finite Differencee Schemes and the Applications[J].Applied Mathematics and Mechanics,1995,16(1):80-90. |
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| Authors: | Liu Ru-xun Zhou Zhao-hui |
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| 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 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. |
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| Keywords: | finite differeuce scheme remainder effect gronp velocity |
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