This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with time-dependent coefficients. Using these regularity results and a perturbation argument of freezing the diffusion coefficient, we prove that the convolution quadrature generated by the second-order backward differentiation formula, with proper correction at the first time step, can achieve second-order convergence for both nonsmooth initial data and incompatible source term. Numerical experiments are consistent with the theoretical results.

中文翻译：

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具有时间相关系数的子扩散：改进的规律性和二阶时间步长

本文涉及具有时间相关扩散系数的子扩散方程的二阶时间离散化。为具有时间相关系数的子扩散方程建立了高阶可微性和正则性估计。使用这些规律性结果和冻结扩散系数的扰动参数，我们证明了由二阶向后微分公式生成的卷积求积，在第一时间步进行适当的校正，可以实现两个非光滑初始数据的二阶收敛和不兼容的源术语。数值实验与理论结果一致。