高阶紧凑差分格式用于修正的异常亚扩散方程
High-order Compact Difference Schemes for the Modified Anomalous Subdiffusion Equation
AI总结：
本文提出两种高阶紧凑有限差分格式用于二阶导数，基于分数中心差分算子建立二阶数值方案，用于修正的异常亚扩散方程，分析了差分格式的可解性、稳定性及收敛性，得出收敛阶为O(τ²+h⁶)和O(τ²+h⁸)的数值方案，并通过数值实验验证理论分析。
摘要：
本文提出两种高阶紧凑有限差分格式用于二阶导数。然后基于分数中心差分算子建立二阶数值方案用于Riemann-Liouvile导数。我们将这些方法应用于分数异常亚扩散方程，构建了两种新型数值方案。通过傅里叶方法详细研究了这些差分格式的可解性、稳定性和收敛性分析。这些数值方案的收敛阶分别为O(τ²+h⁶)和O(τ²+h⁸)。最后展示了数值实验，结果与理论分析一致。
英文摘要：
In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference operator. We apply these methods to fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability and convergence analysis of these difference schemes are studied by Fourier method in details. The convergence orders of these numerical schemes are $\mathcal {O}(τ^2+h^6)$ and $\mathcal {O}(τ^2+h^8)$, respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.
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