| 一类扩散方程Dirichlet问题概率数值解法 |
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| 引用本文： | 吴冬生,刘梅亭. 一类扩散方程Dirichlet问题概率数值解法[J]. 河北大学学报(自然科学版), 1996, 0(4) |
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| 作者姓名： | 吴冬生 刘梅亭 |
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| 作者单位： | 河北大学数学系(吴冬生)，华北水利水电学院基础部(刘梅亭) |
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| 摘 要： | 本文就如下扩散方程Ｄｉｒｉｃｈｌｅｔ问题ｕｔ＝１２△ｕ＋ｑ（ｘ）ｕｘ∈Ｄｕ｜Ｄ＝φ（ｘ）｛（这里ＤＲｄ为ｄ＋１维欧氏空间中有界区域，ｑ（ｘ）是定义在Ｄ的有界Ｈｏｌｄｅｒ连续函数，φ为Ｄ可测函数）通过模拟时空布朗运动及应用Ｍｏｎｔｅ－Ｃａｒｌｏ方法给出了其概率数值解，并在依概率意义下证明了概率数值解收敛到其概率解。
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| 关 键 词： | 时空布朗运动 概率数值解 Monte－Carlo方法 |
Probability Numerical Solution for the Dirichlet Problem in a Class of Diffusion Equation |
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| Wu Dongsheng. Probability Numerical Solution for the Dirichlet Problem in a Class of Diffusion Equation[J]. Journal of Hebei University (Natural Science Edition), 1996, 0(4) |
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| Authors: | Wu Dongsheng |
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| Abstract: | In this paper,we studied the Dirichlet problem of diffusion equation u t=12△u+qu on u| =φ(Ⅰ) (where is a bounded domain of d+1-dimensional Euclidean space d,is its boundary,q is a bounded Holder continous function on ,φ is a measure funation on ) Through analog standard Space-Time Brown motion and using Monte-Calo method,Probability numerical solution of (Ⅰ) is given.At last,we proved the probability numberical solution coverges to its probability solution in probability. |
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| Keywords: | Standard space-time brown motion Probability numberical solution Monte-Carlo method |
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