Finite Difference Approximation for Two-Dimensional Time Fractional Diffusion Equation-Reference-Cited by-同舟云学术

Finite Difference Approximation for Two-Dimensional Time Fractional Diffusion Equation

Published:2007-01 Issue:1 Volume:1 Page:1-16
ISSN:1748-3026
Container-title:Journal of Algorithms & Computational Technology
language:en
Short-container-title:Journal of Algorithms & Computational Technology

Author:

Zhuang P.¹,Liu F.¹²

Affiliation:

1. School of Mathematical Sciences, Xiamen University, China

2. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

Abstract

Fractional diffusion equations have recently been used to model problems in physics, hydrology, biology and other areas of application. In this paper, we consider a two-dimensional time fractional diffusion equation (2D-TFDE) on a finite domain. An implicit difference approximation for the 2D-TFDE is presented. Stability and convergence of the method are discussed using mathematical induction. Finally, a numerical example is given. The numerical result is in excellent agreement with our theoretical analysis.

Publisher

SAGE Publications

Link

http://journals.sagepub.com/doi/pdf/10.1260/174830107780122667

Reference19 articles.

1. Time-fractional telegraph equations and telegraph processes with brownian time

2. Least squares finite-element solution of a fractional order two-point boundary value problem

3. Fractional diffusion equation and relaxation in complex viscoelastic materials

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