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The subdiffusion equations with a Caputo fractional derivative of order$\alpha \in (0,1)$ arise in a wide variety of practical problems, which isdescribing the transport processes, in the force-free limit, slower thanBrownian diffusion. In this work, we derive the correction schemes of theLagrange interpolation with degree $k$ ($k\leq 6$) convolution quadrature,called $L_k$ approximation, for the subdiffusion, which are easy to implementon variable grids. The key step of designing correction algorithm is tocalculate the explicit form of the coefficients of $L_k$ approximation by thepolylogarithm function or Bose-Einstein integral. To construct a $\tau_8$approximation of Bose-Einstein integral, the desired $(k+1-\alpha)$th-orderconvergence rate can be proved for the correction $L_k$ scheme with nonsmoothdata, which is higher than $k$th-order BDF$k$ method in [Jin, Li, and Zhou,SIAM J. Sci. Comput., 39 (2017), A3129--A3152; Shi and Chen, J. Sci. Comput.,(2020) 85:28]. The numerical experiments with spectral method are given toillustrate theoretical results.

Correction of high-order $L_k$ approximation for subdiffusion