The goal of this paper is to prove the theory that the L1 scheme for solving time fractional partial differential equations with nonsmooth data has the uniform $l^1$ optimal order error estimate. For the L1 scheme combined with the first-order convolution quadrature scheme, by using Laplace transform rules we obtain the uniform $l^1$ long time convergence of the L1 scheme for smooth and nonsmooth initial data with of Lubich with first-order accuracy in the homogeneous case. In earlier work, various authors studied the convergence properties of the L1 scheme for smooth and nonsmooth initial data in both the homogeneous and inhomogeneous cases. However, their convergence does not apply to the uniform $l^1$ long time convergence behavior.

本文的目的是证明求解具有非光滑数据的时间分数阶偏微分方程的 L1 方案具有一致的理论 ${升}^1$最优顺序误差估计。对于结合一阶卷积正交方案的 L1 方案，通过使用拉普拉斯变换规则，我们得到了均匀的${升}^1$用于平滑和非平滑初始数据的 L1 方案在齐次情况下具有一阶精度的 Lubich 的长时间收敛。在早期的工作中，许多作者研究了齐次和非齐次情况下平滑和非平滑初始数据的 L1 方案的收敛特性。然而，它们的收敛性不适用于统一${升}^1$ 长时间的收敛行为。