Functional Differential Equations (FDE) and Boundary Heat Equation (BHE)

该数据集包含了两个适用于数值实验的函数微分方程（FDEs），因为它们具有可用的解析解，这使得研究者能够计算绝对误差和相对误差。这些误差计算是偏微分方程（PDEs）和函数微分方程数值分析中的主要评价指标。通过该数据集，实验展示了典型的物理信息神经网络（PINNs）的相对误差大约在10^-3的量级。该任务旨在对函数微分方程进行数值分析。

This dataset contains two functional differential equations (FDEs) tailored for numerical experiments. These equations have readily available analytical solutions, enabling researchers to calculate both absolute and relative errors. Such error computations serve as the primary evaluation metrics in the numerical analysis of partial differential equations (PDEs) and functional differential equations. Experiments using this dataset demonstrate that the relative error of typical Physics-Informed Neural Networks (PINNs) is approximately on the order of 10^-3. This task aims to conduct numerical analysis on functional differential equations.