The modified anomalous subdiffusion equation plays an important role in the modeling of the processes that become less anomalous as time evolves. In this paper, we consider the efficient difference scheme for solving such time-fractional equation in two space dimensions. By using the modified L1 method and the compact difference operator with fast discrete sine transform technique, we develop a fast Crank-Nicolson compact difference scheme which is proved to be stable with the accuracy of . Here, and are the fractional orders which both range from 0 to 1, and and are, respectively, the temporal and spatial stepsizes. We also consider the method of adding correction terms to efficiently deal with the nonsmooth problems. Numerical examples are provided to verify the effectiveness of the proposed scheme.

中文翻译：

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基于快速离散正弦变换的修正的异常扩散方程的快速高阶差分格式

修改后的异常扩散子方程在过程建模中起着重要作用，随着时间的流逝，异常过程变得越来越少。在本文中，我们考虑了在两个空间维度上求解此类时间分数方程的有效差分方案。通过使用改进的L1方法和具有快速离散正弦变换技术的紧致差分算子，我们开发了一种快速的Crank-Nicolson紧致差分方案，该方案被证明是稳定的，并且精度为。在这里，和是分数阶，它们都在0到1的范围内，并且和分别是时间和空间步长。我们还考虑了添加校正项以有效处理非平滑问题的方法。数值算例验证了所提方案的有效性。