%0 Journal Article
%T 空间分布阶时间分数阶扩散方程的有限体积法<br>Finite Volume Method for a Space Distributed-Order Time-Fractional Diffusion Equation
%A 杨莹莹
%A 李景
%J Pure Mathematics
%P 351-361
%@ 2160-7605
%D 2019
%I Hans Publishing
%R 10.12677/PM.2019.93047
%X <div style=\"text-align:justify;\">
	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。<br />
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.
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%K 空间分布阶方程，时间分数阶扩散方程，有限体积法，稳定性和收敛性<br>Space Distributed-Order Equation
%K Time-Fractional Diffusion Equation
%K Finite Volume Method
%K Stability and Convergence
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=30297