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

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。

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.