Numerical simulations of 2D fractional subdiffusion problems
Numerical simulations of 2D fractional subdiffusion problems
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DOI：
10.1016/j.jcp.2010.05.015
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
H. Brunner;Leevan Ling;Masahiro Yamamoto
中科院分区：
文献类型：
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作者：
H. Brunner;Leevan Ling;Masahiro Yamamoto
分数导数在科学和工程的各个领域中的应用越来越多，这表明对于具有真实对象和过程的模型，存在着对更好的数学算法的巨大需求。目前，由于分数阶导数的记忆效应，大多数算法都是针对一维问题而设计的。在这项工作中，二维分数次扩散问题的求解采用了自适应时间步长和自适应空间基选择相结合的算法。文中还用该算法模拟了一个次扩散-对流方程。
The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.