时空分数阶对流扩散方程的两种有限差分格式的比较（英文）

A comparison of two kinds of finite difference schemes for space-time fractional convection-diffusion equations

提出了求解有限区域上的一维时空分数阶变系数对流扩散方程的两种隐式有限差分格式,就格式的精度和收敛阶比较这两种差分格式的优劣.当使用Caputo分数阶导数对a阶时间导数项进行离散时,在两个不同的点上分别采用中心差分,而对β阶空间导数项均使用转化的Grünwald公式进行离散.对得到的两种格式进行稳定性和收敛性分析.用几个已知精确解的数值例子验证和比较这两种有限差分格式的精确性和有效性.

Two implicit finite difference schemes were developed for solving one dimensional space-time fractional convection-diffusion equations with variable coefficients on a finite domain,and our purpose was to compare these two finite difference schemes in terms of the accuracy and convergence order of the scheme.We took advantage of the central difference at two different points respectively,when we discretized the temporal α-order derivative term using Caputo fractional order derivative.The spatial β-order derivative term was discretized by using a shifted Grünwald formula.Analysis of stability and convergence of the methods were done.Numerical examples with known exact solution were used to verify and compare the finite difference schemes.