Numerical solution of two-dimensional fractional diffusion equations by a high-order ADI method
Numerical solution of two-dimensional fractional diffusion equations by a high-order ADI method
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DOI：
10.1685/journal.caim.421
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发表时间：
2013-03
影响因子：
1.3
通讯作者：
M. Concezzi;R. Spigler
中科院分区：
文献类型：
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作者：
M. Concezzi;R. Spigler
一些感兴趣的数学模型，例如，对于气象学，可以用具有时间和/或空间分数导数的扩散方程来表示。通常的时间导数可以被替代，例如，所谓的Caputo分数导数（阶数γ ∈（0，1）），而空间导数可以写成Riemann-Liouville分数导数（阶数α ∈（1，2））。在本文中，我们实现三阶精度的时间数值算法来解决二维分数阶扩散方程。这些是新的有限差分格式，Gr nwald-Letnikov差分算子u和一些ADI方法的基础上，结合优化的外推策略。数值例子，关于模型问题以及现实世界中的应用，给出。
Some mathematical models of interest, e.g., for Meteorology, can be formulated in terms of diffusion equations with time and/or space fractional derivatives. The usual time derivative can be replaced, for instance, by the so-called Caputo fractional derivative (of order γ ∈ (0, 1)), while the space derivatives can be written as a Riemann-Liouville fractional derivatives (of order α ∈ (1, 2)). In this paper, we implement third-order accurate in time numerical algorithms to solve two-dimensional fractional diffusion equations. These are new finite difference schemes, based on the Gr nwald-Letnikov difference operator u and some ADI methods, combined with an optimized extrapolation strategy. Numerical examples, concerning model-problems as well as real-world applications, are given.