| 一类半线性方程Dirichlet问题概率数值解法 |
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| 引用本文： | 吴冬生,孙玉芝.一类半线性方程Dirichlet问题概率数值解法[J].河北大学学报(自然科学版),1996(1). |
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| 作者姓名： | 吴冬生 孙玉芝 |
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| 作者单位： | Department of Mathematics，Hebei University，Baoding 071002 |
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| 摘 要： | 本文讨论了如下半线性方程Ｄｉｒｉｃｈｌｅｔ问题的概率数值解法。其中为有界区域，ｃ（ｘ）是Ｄ上有界Ｈｏｌｄｅｒ连续函数，ｆ（ｘ，ｚ）（ｘ∈Ｄ，ｚ∈Ｒ１）是满足一定光滑性的非线性函数，（ｘ）为Ｄ上可测函数。通过模拟Ｂｒｏｗｎ运动及应用Ｍｏｎｔｅ—Ｃａｒｌｏ方法，得到方程（Ⅰ）的概率数值解迭代公式，进一步在依概率意义下证明了其概率数值解收敛到其解。
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| 关 键 词： | 半线性方程，概率数值解，Monte—Carlo方法 |
Probability Numerical Solution to the Dirichlet Problem of Qusi-linear Equation |
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| Wu Dongsheng, Sun Yuzhi.Probability Numerical Solution to the Dirichlet Problem of Qusi-linear Equation[J].Journal of Hebei University (Natural Science Edition),1996(1). |
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| Authors: | Wu Dongsheng Sun Yuzhi |
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| Abstract: | In this paper, using analogue Brown Motion and Monte-Carlo method, we obtained the itreation formula of probability numerical solution to the Dirichlet problem of the qusi-linear equation where D Rd is a bounded area. c(x) is a bounded H lder continous function on D,f(x,z)(x∈D, z∈R1 is a nonlinear sufficient smooth function. (x)is a measurable function on D, Furthermore, we proved the probability itreation numerical solution converges to its solution in probability |
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| Keywords: | Qusi-linear equation Probability numerical solution Monte-Carlo method |
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