关键词: 二维时间分数阶扩散方程, 交替分带 Crank-Nicolson 差分格式, 稳定性；并行计算；数值实验

Abstract: The fractional anomalous diffusion equation has profound physical background and rich theoretical connotation, and its numerical methods are of important scientific significance and engineering application value. For the two-dimensional time fractional anomalous diffusion equation, an alternating band Crank-Nicolson difference parallel computing method (ABdC-N method) is studied in this paper. Based on the alternating segment technology, the ABdC-N scheme is constructed from the classic explicit scheme, implicit scheme and Crank-Nicolson difference scheme. It can be seen from both theoretical analyses and numerical experiments that the ABdC-N method is unconditionally stable and convergent. This method has good characteristics of parallel computing, and its computation efficiency is much higher than the classical serial differential method. Our results thus show that the ABdC-N difference method is effective for solving the two-dimensional time fractional anomalous diffusion equation.

Key words: two-dimensional time fractional diffusion equation, alternating band Crank-Nicolson difference scheme, stability, parallel computation, numerical experiments