Numerical methods and analysis for a class of fractional advection-dispersion models
Numerical methods and analysis for a class of fractional advection-dispersion models
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DOI：
10.1016/j.camwa.2012.01.020
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
Fawang Liu;P. Zhuang;K. Burrage
中科院分区：
文献类型：
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作者：
Fawang Liu;P. Zhuang;K. Burrage
本文研究了一类分数阶对流-弥散模式。这些模式包括五个分数阶对流扩散模式，即时间FADM、时间Caputo分数导数为0<；γ<；1的移动/静止时间FADM、具有两侧Riemann-Liouville导数的空间FADM、时间-空间FADM和指数为1<；γ<；2的时间分数阶对流扩散波模式。这些方程可用于模拟具有重尾的区域尺度异常弥散。对于这些FADM，我们提出了计算上有效的隐式数值方法。系统地分析和比较了隐式数值方法的稳定性和收敛性能。最后，给出了一些结果，验证了理论分析的有效性。
In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0<γ<1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1<γ<2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.