Numerical simulations of 2D fractional subdiffusion problems

被引：109

作者：

Brunner, Hermann ^{[1
]}

Ling, Leevan ^{[1
]}

Yamamoto, Masahiro ^{[2
]}

机构：

[1] Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China

[2] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2010年 / 229卷 / 18期

关键词：

Fractional differential equations; Kansas method; Radial basis functions; Collocation; Adaptive greedy algorithm; Geometric time grids; BOUNDARY-VALUE-PROBLEMS; DIFFERENCE APPROXIMATION; RANDOM-WALK; DIFFUSION; EQUATIONS; ALGORITHMS;

D O I：

10.1016/j.jcp.2010.05.015

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：6613 / 6622

页数：10

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