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.

中文翻译：

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具有诺伊曼边界条件的线性反应亚扩散方程的最优估计

在本文中，我们应用经典的非均匀L1公式和紧致差分格式来求解具有诺伊曼边界条件的线性分式系统。提出了一种新颖且简单的离散最大范数收敛分析的演示策略。此外，基于所得系数矩阵的特殊性质，采用对角化技术和离散余弦变换（DCT）来加快该方法的收敛速度。此外，数值方案还扩展到三维（3D）情况。给出了几个数值实验来支持我们的发现。