| 微分方程基于聚类分析的自适应差分格式 |
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| 引用本文： | 陈静,王景亮,罗振东. 微分方程基于聚类分析的自适应差分格式[J]. 内蒙古大学学报(自然科学版), 2011, 42(1): 32-39 |
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| 作者姓名： | 陈静 王景亮 罗振东 |
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| 作者单位： | 1. 中国农业大学理学院应用数学系,北京,100083
2. 华北电力大学数理学院,北京,102206 |
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| 基金项目： | 国家自然科学基金，中央高校基本业务费专项资金资助项目 |
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| 摘 要： | 通过聚类分析找出一般差分格式的数值解出现数值信息波动大的区域,自适应地进行网格加密,构造出高精度的自适应差分格式.数值试验结果表明,这种新算法较一般差分格式能显著地减少数据存储量和计算量,提高差分格式的稳定性和数值解的精度.
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| 关 键 词： | 聚类分析 差分格式 数据预处理 自适应 |
A Kind of the Difference Scheme Based on Cluster Analysis for Differential Equations |
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| CHEN Jing,WANG Jing-liang,LUO Zhen-dong. A Kind of the Difference Scheme Based on Cluster Analysis for Differential Equations[J]. Acta Scientiarum Naturalium Universitatis Neimongol, 2011, 42(1): 32-39 |
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| Authors: | CHEN Jing WANG Jing-liang LUO Zhen-dong |
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| Affiliation: | CHEN Jing1,WANG Jing-liang1,LUO Zhen-dong2(1.Department of Applied Mathematics,College of Science,China Agricultural University,Beijing 100083,China,2.School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China) |
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| Abstract: | The fields of the fluctuation information of numerical solutions of the difference scheme for differential equations based on a cluster analysis are found,the node points of these fields are self-adaptively refined,and some new self-adaptive difference schemes with high-accuracy for differential equations are obtained.Numerical results show that compared with general difference schemes,the new difference scheme algorithms can significantly reduce data storage,computing time and improve the stability of diff... |
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| Keywords: | cluster analysis difference scheme data preprocess self-adapted |
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