| 自适应网格下齐次奇异摄动问题的一致收敛性分析 |
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| 引用本文： | 孙力楠,王安涛. 自适应网格下齐次奇异摄动问题的一致收敛性分析[J]. 兰州理工大学学报, 2011, 37(5): 131-136 |
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| 作者姓名： | 孙力楠 王安涛 |
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| 作者单位： | 1. 信息工程大学测绘学院,河南郑州,450052
2. 河南省开封人民警察学校计算机教研室,河南开封,475000 |
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| 摘 要： | 利用自适应移动网格方法求解齐次奇异摄动边值问题,通过常数与解的一阶导数幂的线性组合构造控制函数来进行网格自适应,分析齐次奇异摄动边值问题在此自适应非均匀网格上的收敛性.利用极值原理证明离散问题解的存在唯一性.对离散问题的数值解及其分段线性插值进行误差估计,分别得到一个与ε无关的一阶误差界.有效地解决齐次奇异摄动方程难以...
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| 关 键 词： | 奇异摄动 自适应网格 迎风格式 误差估计 |
Uniform convergence analysis of homogenous singular perturbation problem with adaptive grids |
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| SUN Li-nan,WANG An-tao. Uniform convergence analysis of homogenous singular perturbation problem with adaptive grids[J]. Journal of Lanzhou University of Technology, 2011, 37(5): 131-136 |
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| Authors: | SUN Li-nan WANG An-tao |
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| Affiliation: | SUN Li-nan1,WANG An-tao2(1.Institute of Surveying and Mapping,Information Engineering University,Zhengzhou 450052,China,2.Computer Teching and Research Section,Kaifeng People's police Academy of Henan,Kaifeng 475000,China) |
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| Abstract: | A homogenous singular perturbation boundary value problem was solved numerically by using the adaptive-moving mesh method,and the adaptive grid was suggested according to a control function,which was a linear combination of a constant floor and a power of the first derivative of the solution.The convergence of the homogenous singular perturbation boundary value problem was analyzed with this adaptive grid.The extremum principle was used to prove the existence and uniqueness of the solutions of its discrete ... |
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| Keywords: | singular perturbation adaptive grid upwind scheme error estimate |
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