| Dirichlet外问题的概率数值方法 |
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| 引用本文： | 唐立,黄立宏,杨文胜.Dirichlet外问题的概率数值方法[J].数学年刊A辑(中文版),2005(4). |
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| 作者姓名： | 唐立 黄立宏 杨文胜 |
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| 作者单位： | 湖南大学数学博士后流动站，湖南大学数学与计量经济学院，中南大学数学科学与计算技术学院 长沙 410082 中南大学数学科学与计算技术学院，长沙 410075，长沙 410082，长沙 410075 |
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| 基金项目： | 国家自然科学基金(No．19871027)
中南大学文理研究基金资助的项目． |
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| 摘 要： | 针对定解区域是无界区域的Dirichlet外问题,提出了一种新的有效的概率数值方法,它是从解的随机表达式出发,将无界区域上的问题转化成区域边界上的问题.此时,只要在边界上进行剖分,将问题离散化,然后在无界区域外的有界区域内构作一个辅助球,并且利用布朗运动、漂移布朗运动从球外一点出发,首中球面的位置和时间的分布等,就可以获得Dirichlet外问题的数值解.
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| 关 键 词： | Dirichlet外问题 布朗运动 漂移布朗运动 首中时分布 |
PROBABILISTIC NUMERICAL METHOD FOR THE EXTERIOR DIRICHLET PROBLEM |
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| TANG Li HUANG Lihong YANG Wensheng Postdoctoral Scientific Research of Mathematics,Hunan University,Changsha ,China, School of Mathematical Sciences and Computing Technology. Central South University,Changsha ,China. College of Mathematics and Econometrics,Hunan University,Changsha ,China. School of Mathematical Sciences and Computing Technology,Central South University,Changsha ,China..PROBABILISTIC NUMERICAL METHOD FOR THE EXTERIOR DIRICHLET PROBLEM[J].Chinese Annals of Mathematics,2005(4). |
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| Authors: | TANG Li HUANG Lihong YANG Wensheng Postdoctoral Scientific Research of Mathematics Hunan University Changsha China School of Mathematical Sciences and Computing Technology Central South University Changsha China College of Mathematics and Econometrics Hunan University Changsha China School of Mathematical Sciences and Computing Technology Central South University Changsha China |
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| Institution: | TANG Li HUANG Lihong YANG Wensheng Postdoctoral Scientific Research of Mathematics,Hunan University,Changsha 410082,China, School of Mathematical Sciences and Computing Technology. Central South University,Changsha 410075,China. College of Mathematics and Econometrics,Hunan University,Changsha 410082,China. School of Mathematical Sciences and Computing Technology,Central South University,Changsha 410075,China. |
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| Abstract: | Domains for the exterior Dirichlet problem are unbounded. Now a new efficient probabilistic numerical method is proposed. It bases on the stochastic representations of solutions and make the problem over unbounded domains turned into a problem over boundary. Subdivision over boundary is needed to make the problem discretized. An auxiliary ball is constructed in the bounded domain outside the unbounded. The distributions of the time and place of hitting spheres for Brownian motion or Brownian motion with drift from outside spheres is emplored to gain the numerical solution. |
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| Keywords: | Exterior Dirichlet problem Brownian motion Brownian motion with drift Distributions of the time |
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