We consider the $L2-1_\sigma$ scheme for subdiffusion of variable exponent. In existing works, determining the superconvergence points requires solving a nonlinear equation relate to the variable exponent at each time step. This work relaxes the selection criterion of superconvergence points without affecting the numerical accuracy, which may reduce the cost of determining superconvergence points. Then we prove error estimates for the $L2-1_\sigma$ scheme of variable-exponent subdiffusion. Numerical results are performed to substantiate the theoretical findings.

翻译：本文研究变指数次扩散方程的$L2-1_σ$数值格式。在现有研究中，确定超收敛点需要在每个时间步求解与变指数相关的非线性方程。本工作在不影响数值精度的前提下放宽了超收敛点的选取准则，从而降低了确定超收敛点的计算成本。随后，我们证明了变指数次扩散方程$L2-1_σ$格式的误差估计。数值实验验证了理论结果的有效性。