Shi, JiankangChen, MinghuaYan, YubinCoa, Jianxiong2022-11-102022-11-102022-09-07Shi, J., Chen, M., Yan, Y., & Coa, J. (2022). Correction of high-order Lk Approximation for Subdiffusion. Journal of Scientific Computing, 93, 31. https://doi.org/10.1007/s10915-022-01984-80885-747410.1007/s10915-022-01984-8http://hdl.handle.net/10034/627291This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10915-022-01984-8The subdiffusion equations with a Caputo fractional derivative of order $\alpha \in (0, 1)$ arise in a wide variety of practical problems, which describe the transport processes, in the force-free limit, slower than Brownian diffusion. In this work, we derive the correction schemes of the Lagrange interpolation with degree $k ( \leq 6)$ convolution quadrature, called $L_{k}$ approximation, for the subdiffusion. The key step of designing correction algorithm is to calculate the explicit form of the coefficients of $L_{k}$ approximation by the polylogarithm function or Bose-Einstein integral. To construct a $\tau_{8}$ approximation of Bose-Einstein integral, the desired $(k+1-\alpha)$th-order convergence rate can be proved for the correction $L_{k}$ scheme with nonsmooth data, which is higher than kth-order BDFk 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 to illustrate theoretical results.https://creativecommons.org/licenses/by-nc-nd/4.0/SubdiffusionNonsmooth dataLaplace transform methodError estimatesArticle1573-7691Journal of Scientific Computing