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This article concerns second-order time discretization of subdiffusionequations with time-dependent diffusion coefficients. High-orderdifferentiability and regularity estimates are established for subdiffusionequations with time-dependent coefficients. Using these regularity results anda perturbation argument of freezing the diffusion coefficient, we prove thatthe convolution quadrature generated by the second-order backwarddifferentiation formula, with proper correction at the first time step, canachieve second-order convergence for both nonsmooth initial data andincompatible source term. Numerical experiments are consistent with thetheoretical results.

Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping