| 调和方程边值问题的高效配置算法 |
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| 引用本文： | 刘经洪,刘灿,朱起定.调和方程边值问题的高效配置算法[J].湖南科技大学学报(自然科学版),2004,19(4):92-94. |
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| 作者姓名： | 刘经洪 刘灿 朱起定 |
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| 作者单位： | 1. 湖南师范大学,数学与计算机科学学院,湖南,长沙,410081
2. 湖南涉外经济职业学院,公共课部,湖南,长沙,410205 |
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| 摘 要： | 首先给出了用Poisson积分公式表示的调和方程边值问题的解.然后利用延拓思想将一般区域上的问题转化为圆域上的问题,进而获得了所需的Poisson积分方程.最后,介绍了求解调和方程边值问题的线性配置算法,并证明了这种算法具有至少 O(h4)精度的逐点强超收敛性.表1,参9.
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| 关 键 词： | 调和方程 边界元 延拓思想 配置算法 Poisson积分方程 强超收敛 |
| 文章编号： | 1672-9102(2004)04-0092-03 |
| 修稿时间： | 2004年6月28日 |
An efficient collocation method for solving boundary value problems of harmonic equations |
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| LIU Jing-hong,LIU Can,ZHU Qi-ding.An efficient collocation method for solving boundary value problems of harmonic equations[J].Journal of Hunan University of Science & Technology(Natural Science Editon),2004,19(4):92-94. |
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| Authors: | LIU Jing-hong LIU Can ZHU Qi-ding |
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| Institution: | LIU Jing-hong~1,LIU Can~2,ZHU Qi-ding~1 |
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| Abstract: | This paper first gives the solutions represented by Poisson integral formulas to the boundary value problems of harmonic equations.Then using extension idea,we transforms the problem on the common domain to that on the circular domain,and further obtains the Poisson integral equation needed.Finally,we introduces a linear collocation method for solving boundary value problems of harmonic equations,and proves that this method possesses ultraconvergence with at least O(h~4) accuracy in the pointwise sense.1tab.9refs. |
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| Keywords: | harmonic equations boundary elements extension idea collocation methods poisson integral equation ultraconvergence |
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