Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
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DOI：
10.1007/s10915-013-9756-2
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发表时间：
2013-07
影响因子：
2.5
通讯作者：
Ya-nan Zhang;Zhi‐zhong Sun
中科院分区：
文献类型：
--
作者：
Ya-nan Zhang;Zhi‐zhong Sun
本文提出了一种 Crank-Nicolson 型紧凑 ADI 方案来求解二维分数次扩散方程。严格证明了该格式的独特可解性、无条件稳定性和收敛性。提出了两个误差估计。一种是标准范数，其中 是时间网格大小， 是空间网格大小；另一个是innorm，与黎曼-刘维尔分数积分算子相关的广义范数。给出的数值结果支持理论分析。
In this paper, a Crank–Nicolson-type compact ADI scheme is proposed for solving two-dimensional fractional subdiffusion equation. The unique solvability, unconditional stability and convergence of the scheme are proved rigorously. Two error estimates are presented. One isin standardnorm, whereis the temporal grid size andare spatial grid sizes; the other isinnorm, a generalized norm which is associated with the Riemann–Liouville fractional integral operator. Numerical results are presented to support the theoretical analysis.