Abstract Uncertain heat equation (for short, UHE) is a type of second-order uncertain PDEs driven by Liu processes. In most cases, since it is tough to get the analytic solution for a UHE, we must find a way to obtain its numerical solution. A forward difference scheme has been designed to solve UHE, but our paper will show that this method may exhibit instability in some situations. We explore another approach, unconditionally stable and namely Dufort-Frankel method. Moreover, this paper will use Dufort-Frankel method to calculate the expected value and extreme value of the solution for a UHE.

中文翻译：

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一维不确定热方程的Dufort-Frankel格式

摘要 不确定热方程（简称UHE）是一种由Liu过程驱动的二阶不确定偏微分方程。在大多数情况下，由于 UHE 的解析解很难得到，我们必须找到一种方法来获得它的数值解。已经设计了一种前向差分方案来解决 UHE，但我们的论文将表明该方法在某些情况下可能会表现出不稳定性。我们探索另一种方法，无条件稳定，即 Dufort-Frankel 方法。此外，本文将使用 Dufort-Frankel 方法计算 UHE 解的期望值和极值。