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Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

Liu, Q. & Liu, Fawang (2009) Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives. Mathematica Numerica Sinica, 31(2).

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Abstract

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

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ID Code: 29787
Item Type: Journal Article
Additional Information: Access to the accepted manuscript version is currently restricted pending permission from the publisher. For more information, please refer to the journal’s website (see Official URL) or contact the author.
Keywords: Non-continuous Seepage Flow, Alternating Direction Method, Fractional Derivative, Stability, Convergence
ISSN: 0245-7791
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2009 Scientific Information Consultants Ltd.
Deposited On: 20 Jan 2010 10:46
Last Modified: 01 Mar 2012 00:05

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