论文标题
与时间相关系数的细胞扩散：提高规律性和二阶阶梯
Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
论文作者
论文摘要
本文涉及与时间相关扩散系数的二阶时间离散化。建立了具有时间依赖系数的子扩散方程的高阶不同性和规律性估计值。使用这些规律性结果以及冻结扩散系数的扰动参数，我们证明由二阶向后分化公式产生的卷积正交正交在第一个时间步骤中进行适当的校正，可以实现二阶收敛的非光齿初始数据和不兼容的源项。数值实验与理论结果一致。
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.
