空间分布阶时间分数阶扩散方程的有限体积法
Finite Volume Method for a Space Distributed-Order Time-Fractional Diffusion Equation
摘要: 本文利用有限体积法研究了空间分布阶时间分数阶扩散方程。首先，用中点求积法将空间分布阶项转化为多项空间分数阶项，利用有限体积法对多项空间分数阶项进行离散。而对于时间分数阶导数，我们采用有限差分法。其次，我们证明了迭代格式的无条件稳定性和收敛性。最后通过一个数值例子来证明算法的有效性。
Abstract: In this paper, the space distributed-order time-fractional diffusion equation is considered. We propose a finite volume method to solve the considered equation. Firstly, we use the mid-point quadrature rule to transform the space distributed-order term into a multi-term fractional term, and the multi-term fractional equation is discretized by the finite volume. For the time-fractional derivative, we apply the finite difference method. We prove that the iterative scheme is uncondi-tionally stable and convergent. A numerical example is presented to verify the effectiveness of the proposed method.
文章引用：杨莹莹, 李景. 空间分布阶时间分数阶扩散方程的有限体积法[J]. 理论数学, 2019, 9(3): 351-361. https://doi.org/10.12677/PM.2019.93047

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