中文摘要：

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．

英文摘要：

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 difference schemes and the accuracy of numerical solutions.