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Abstract：
For usual uncertain heat equations, it is challenging to acquire their analytic solutions. A forward difference Euler method has been used to compute the uncertain heat equations\' numerical solutions. Nevertheless, the Euler scheme is instability in some cases. This paper proposes an implicit task to overcome this disadvantage, namely the Crank-Nicolson method, which is unconditional stability. An example shows that the Crank-Nicolson scheme is more stable than the previous scheme (Euler scheme). Moreover, the Crank-Nicolson method is also applied to compute two characteristics of uncertain heat equation\'s solution-expected value and extreme value. Some examples of uncertain heat equations are designed to show the availability of the Crank-Nicolson method.
摘要：
对于通常的不确定热方程，获得他们的分析解决方案是具有挑战性的。正向差分欧拉方法已用于计算不确定热方程的数值解。然而，欧拉方案在某些情况下是不稳定的。本文提出了一个隐式任务来克服这一缺点，即Crank-Nicolson方法,这是无条件的稳定。一个例子表明，Crank-Nicolson方案比以前的方案（欧拉方案）更稳定。此外，Crank-Nicolson方法还用于计算不确定热方程解的两个特征——期望值和极值。设计了一些不确定热方程的示例，以显示Crank-Nicolson方法的可用性。
