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Published in: Journal of Scientific Computing 3/2016

01-07-2015

Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations

Authors: Guang-hua Gao, Zhi-zhong Sun

Published in: Journal of Scientific Computing | Issue 3/2016

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Abstract

Two alternating direction implicit difference schemes are derived for two-dimensional distributed-order fractional diffusion equations. It is proved that the schemes are unconditionally stable and convergent in a discrete \(L^1(L^\infty )\) norm with the convergence orders \(O(\tau ^2|\ln \tau |+h_1^2+h_2^2+\Delta \alpha ^2)\) and \(O(\tau ^2|\ln \tau |+h_1^4+h_2^4+\Delta \alpha ^4),\) respectively, where \( \tau , h_i \;(i=1,2)\) and \(\Delta \alpha \) are the step sizes in time, space and distributed order. Several numerical examples are given to confirm the theoretical results.

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Metadata
Title
Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations
Authors
Guang-hua Gao
Zhi-zhong Sun
Publication date
01-07-2015
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-015-0064-x

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