Numerical solution of time fractional diffusion systems

被引：39

作者：

Burrage, Kevin ^{[1
,2
,3
,4
]}

Cardone, Angelamaria ^{[5
]}

D'Ambrosio, Raffaele ^{[5
]}

Paternoster, Beatrice ^{[5
]}

机构：

[1] Queensland Univ Technol, Brisbane, Qld, Australia

[2] Univ Oxford, Dept Comp Sci, Oxford OX1 3QD, England

[3] Queensland Univ Technol, ARC Ctr Excellence Math & Stat Frontiers, Brisbane, Qld 4000, Australia

[4] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4000, Australia

[5] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II 132, I-84084 Salerno, Italy

来源：

APPLIED NUMERICAL MATHEMATICS | 2017年 / 116卷

关键词：

Diffusion systems; Fractional differential equations; Spectral methods; Finite-difference schemes; ANOMALOUS DIFFUSION; EQUATION; APPROXIMATION; BEHAVIOR; TISSUE; DOMAIN;

D O I：

10.1016/j.apnum.2017.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one. For the numerical solution, a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time. The spectral method considerably reduces the computational cost with respect to step-by-step methods to discretize the fractional derivative. Some classes of spectral bases are considered, which exhibit different convergence rates and some numerical results based on time diffusion reaction diffusion equations are given. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：82 / 94

页数：13

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