Superlinearly convergent algorithms for the two-dimensional spaceatime CaputoaRiesz fractional diffusion equation

In this paper, we discuss the spaceatime CaputoaRiesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally...

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Bibliographic Details
Published in:Applied numerical mathematics 2013-08, Vol.70, p.22-41
Main Authors: Chen, Minghua, Deng, Weihua, Wu, Yujiang
Format: Article
Language:English
Subjects:
Algorithms
Beta
Diffusion
Finite difference method
Mathematical analysis
Mathematical models
Stability
Two dimensional
Online Access:Get full text
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Summary:In this paper, we discuss the spaceatime CaputoaRiesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally stable (the explicit scheme is conditionally stable with the stability condition theta super( gamma )/( Delta x) super( alpha )+ theta super( gamma )/( Delta y) super( beta ) < C) and 2nd order convergent in space direction, and (2- xi )(2- gamma )th order convergent in time direction, where gamma member of (0,1].
ISSN:0168-9274
DOI:10.1016/j.apnum.2013.03.006