Hadamard分数阶扩散方程的时空Legendre谱方法
The Space-Time Legendre Spectral Method for Hadamard Fractional Diffusion Equations
摘要: 本文主要研究Hadamard时间分数阶扩散方程的时空谱方法，对Hadamard时间分数阶扩散方程在空间方向采用Legendre-Galerkin谱方法构建高效的空间数值求解格式，减少计算成本；在时间上采用Legendre谱配置法进行离散，使得方程在时间和空间上全局离散，得到时空全离散的高精度数值格式。最后通过数值算例求解对其准确性与有效性进行验证。数值实验表明，该方法误差达到10−16，具有优异的谱精度，验证了离散格式的高效性与可靠性。
Abstract: This paper focuses on the space-time spectral method for the Hadamard-type time-fractional diffusion equation. For the spatial discretization of the equation, the Legendre-Galerkin spectral method is adopted to construct an efficient numerical spatial scheme to reduce the computational cost. The Legendre spectral collocation method is employed for temporal discretization, which enables global discretization of the equation in both time and space domains, and yields a fully discrete high-precision space-time numerical scheme. Finally, numerical examples are carried out to verify the accuracy and effectiveness of the proposed method. Numerical results demonstrate that the method achieves an error of 10−16, exhibits excellent spectral accuracy, and validates the high efficiency and reliability of the established discretization scheme.
文章引用：王婧涵, 曹俊英, 王自强. Hadamard分数阶扩散方程的时空Legendre谱方法[J]. 应用数学进展, 2026, 15(6): 274-281. https://doi.org/10.12677/aam.2026.156286

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