Key points are not available for this paper at this time.
A Crank–Nicolson-type difference scheme is proposed for solving the subdiffusion equation with fractional derivative, and the truncation error is analyzed in detail. At each temporal level, only a tridiagonal linear system needs to be solved and the Thomas algorithm may be used. The solvability, unconditional stability, and H¹ norm convergence are proved. The convergence order is min\2-{/2, \;1+\} in the temporal direction and two in the spatial direction. By the Sobolev embedding inequality, we obtain the maximum norm error estimate. A spatial compact scheme based on the Crank–Nicolson-type difference scheme is also presented, and similar results are given. The convergence order is O (^{ min\2-{/2, \;1+\}}+h⁴). Numerical experiments are included to support the theoretical results, and comparisons with the related works are presented to show the effectiveness of our method.
Zhang et al. (Sat,) studied this question.