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Finite difference approximation for two-dimensional time fractional diffusion equation

Zhuang, Pinghui & Liu, Fawang (2007) Finite difference approximation for two-dimensional time fractional diffusion equation. Journal of Algorithms & Computational Technology, 1(1), pp. 1-15.

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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.

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ID Code: 15085
Item Type: Journal Article
Keywords: TWO, DIMENSIONAL TIME FRACTIONAL DIFFERENTIAL EQUAT, IMPLICIT DIFFERENCE APPROXIMATION, STABILITY, CONVERGENCE
DOI: 10.1260/174830107780122667
ISSN: 1748-3018
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Multi-Science Publishing
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 10 Oct 2008
Last Modified: 29 Feb 2012 23:22

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