时间分数阶扩散方程的一种交替分带并行差分方法

An Alternating Band Parallel Difference Method for Time Fractional Diffusion Equation

分数阶反常扩散方程具有深刻的物理背景和丰富的理论内涵,其数值解法的研究具有重要的科学意义和工程应用价值.针对二维时间分数阶反常扩散方程,本文研究一种交替分带 Crank-Nicolson差分的并行计算方法(ABdC-N方法).该格式是在交替分带技术的基础上,结合经典显式、隐式和 Crank-Nicolson差分格式构造而成.理论分析和数值试验表明,ABdC-N方法是无条件稳定和收敛的,具有良好的计算精度和并行计算性质,并且计算效率远优于经典的串行差分方法,证实本文 ABdC-N差分方法求解二维时间分数阶反常扩散方程是有效的.

The fractional anomalous di usion equation has profound physical background and rich theoretical connotation, and its numerical metho ds are of imp ortant scienti c signi cance and engineering application value. F or the two-dimensional time fractional anomalous di usion equation, an alternating band Crank-Nicolson di erence parallel computing metho d (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 di erence scheme. It can b e seen from b oth theoretical analyses and numerical exp eriments that the ABdC-N metho d is unconditionally stable and convergent. This metho d has goo d characteristics of parallel computing, and its computation e ciency is much higher than the classical serial di erential method. Our results thus show that the ABdC-N di erence metho d is e ective for solving the two-dimensional time fractional anomalous di usion equation.