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。
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
出处
《河北大学学报（自然科学版）》
CAS
1996年第1期1-7,共7页
Journal of Hebei University(Natural Science Edition)
