| 边值问题的概率数值方法 |
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| 引用本文： | 唐立,杨文胜.边值问题的概率数值方法[J].数学物理学报(A辑),2008,28(1):81-085. |
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| 作者姓名： | 唐立 杨文胜 |
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| 作者单位： | 中南大学数学科学与计算技术学院,长沙410075 |
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| 基金项目： | 国家自然科学基金
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湖南省高校青年骨干教师培养基金 |
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| 摘 要： | 该文运用概率理论研究了一种有界和无界区域上边值问题的数值方法.其主要思想如下: 先写出所求边值问题解的随机表达方式, 再构造一个辅助球, 并且通过区域边界上的剖分将问题离散化,最后利用漂移布朗族的强马尔可夫性和它的球面首中时、首中位置的分布, 获得离散问题的解.
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| 关 键 词： | 概率数值方法 边值问题 漂移布朗运动 |
| 文章编号： | 1003-3998（2008）01-081-05 |
| 收稿时间： | 2005-10-11 |
| 修稿时间： | 2006-12-30 |
Probabilistic Numerical Method for Boundary Value Problems |
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Tang Li,Yang Wensheng
.Probabilistic Numerical Method for Boundary Value Problems[J].Acta Mathematica Scientia,2008,28(1):81-085. |
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| Authors: | Tang Li Yang Wensheng
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| Institution: | School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075
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| Abstract: | In this paper a kind of numerical method for boundary value problems over bounded or unbounded domains is investigated by probability theory. It's main idea is as follows: Firstly, represent the solution of the boundary value problem as the stochastic representations. Secondly, construct an auxiliary ball and subdivide the boundaries of the domains to make the problem discretized. Finally, by using the strong Markov property and the distributions of the time and place of hitting spheres for Brownian motion with drift, obtain the solutions to the discretized problems. |
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| Keywords: | Probabilistic numerical method Boundary value problem Brownian family with drift |
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