An optimal estimate for linear reaction subdiffusion equations with Neumann boundary conditions

In this paper, we apply classical non-uniform L1 formula and the compact difference scheme for solving linear fractional systems with Neumann boundary conditions. A novelty and simple demonstration strategy is presented on the convergence analysis in the discrete maximum norm. Moreover, based on the special properties of the resulting coefficient matrix, diagonalization technique and discrete cosine transform (DCT) are adopted to speed up the convergence rate of the proposed method. In addition, the numerical scheme is also extended to the three-dimensional (3D) case. Several numerical experiments are given to support our findings.