Sharp H1-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations

A finite difference cosine pseudo-spectral scheme is presented for solving a linear reaction-subdiffusion problem with Neumann boundary conditions. The nonuniform version of L1 formula is employed for approximating the Caputo fractional derivative, and a cosine pseudo-spectral approximation is utilized in spatial discretization. With the help of discrete fractional Grönwall inequality and global consistency analysis, sharp H1-norm error estimate reflecting the regularity of solution is verified for the proposed method. A fast algorithm is implemented in computation and numerical results confirm the sharpness of our analysis.

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