| 引用本文： |
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杨继昌,沈柳平.对流方程GLxF格式数值解振荡的可控性[J].广西科学院学报,2010,26(1):9-12. [点击复制]
- YANG Ji-chang,SHEN Liu-ping.The Controllable Quality of Oscillations in Numerical Solution of GLxF Scheme for Convection-equation[J].Journal of Guangxi Academy of Sciences,2010,26(1):9-12. [点击复制]
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| 摘要: |
| 给出对流方程ut+aux=0,x∈R,t>0,a∈R的广义Lax-Friedrichs格式(GLxF格式)稳定的充要条件,在数值粘性、网格比及初始数据离散点变化时用图例直观展示格式数值解的行为.然后用傅利叶分析法证明GLxF格式数值解的振荡与数值粘性、网格比及初始数据奇偶离散的关系,从理论上论证数值解的振荡是可控的. |
| 关键词: 对流方程 数值解 振荡 傅利叶分析 控制 |
| DOI： |
| 投稿时间：2009-05-20 |
| 基金项目: |
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| The Controllable Quality of Oscillations in Numerical Solution of GLxF Scheme for Convection-equation |
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YANG Ji-chang, SHEN Liu-ping
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| (Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi, 545004, China) |
| Abstract: |
| Stable condition of GLxF scheme for convection-equation ut+aux=0,x∈R,t>0,a∈R is proposed.By some figures, the behavior of numerical solution is intuitively presented when numerical viscosity,ratio of mesh and discrete point of initial data are changed.Then prove the interrelation among oscillation of numerical solution for GLxF scheme,numerical viscosity,ratio of mesh and odd-even discretization of initial data by Fourier analysis is proved.It is theoretically proved that oscilations of numerical solution are controllable. |
| Key words: convection-equation numerical solution oscillations Fourier analysis control |
