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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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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|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|
|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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