Abstract Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the existing time discretization schemes in literature. Without the corrections, the schemes have only a first order of accuracy for both smooth and nonsmooth data. After correcting some starting steps and some weights of the schemes, the optimal convergence orders O(k3–α) and O(k4–α) with 0 < α < 1 can be restored for any fixed time t for both smooth and nonsmooth data, respectively. The error estimates for these two new high-order schemes are proved by using Laplace transform method for both homogeneous and inhomogeneous problem. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

中文翻译：

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非光滑数据子扩散问题的两种高阶时间离散化方案

摘要 在对文献中现有时间离散化方案进行修正的基础上，提出了两种新的高阶时间离散化方案来解决非光滑数据的子扩散问题。如果没有校正，这些方案对于平滑和非平滑数据都只有一级精度。在修正一些起始步骤和方案的一些权重后，对于平滑和非平滑数据，可以在任何固定时间 t 恢复最优收敛阶数 O(k3-α) 和 O(k4-α)，其中 0 < α < 1，分别。对齐次和非齐次问题均采用拉普拉斯变换方法证明了这两种新高阶方案的误差估计。数值算例表明数值结果与理论结果一致。