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Error estimates of Crank-Nicolson-type difference schemes for the subdiffusion equation. (English) Zbl 1251.65132
The authors propose a Crank-Nicolson-type difference scheme for solving the subdiffusion equation with fractional derivative. Only a tridiational linear system needs to be solved at each temporal level. The solvability, unconditional stability, and H 1 norm convergence are proved. The convergence order is min{2-γ/2,1+γ} in the temporal direction and two in the spatial direction. Using the Sobolev embedding inequality, the maximum norm error estimate is obtained. A spatial compact scheme based on the Crank-Nicolson-type difference scheme with the convergence order of O(τ min{2-γ/2,1+γ} +h 4 ) is also presented. Numerical examples support the theoretical analysis. Comparisons with the related existing works are presented to show the effectiveness of the present method. This is an interesting paper.
MSC:
65M15Error bounds (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35R11Fractional partial differential equations
35K05Heat equation