Finite element method is used to approximately solve a class of linear time-invariant, time-fractional-order diffusion equation formulated by the non-classical Fick law and a “long-tail” power kernel. In our derivation, “long-tail” power kernel relates the matter flux vector to the concentration gradient while the power-law relates the mean-squared displacement to the Gauss white noise. This work contributes a numerical analysis of a fully discrete numerical approximation using the space Galerkin finite element method and the approximation property of the Caputo time fractional derivative of an efficient fractional finite difference scheme. Both approximate schemes and error estimates are presented in details. Numerical examples are included to validate the theoretical predictions for various values of order of fractional derivatives.
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ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 30–September 2, 2009
San Diego, California, USA
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4901-9
PROCEEDINGS PAPER
Numerical Approximation and Error Estimation of a Time Fractional Order Diffusion Equation
Changpin Li,
Changpin Li
Shanghai University, Shanghai, China
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Zhengang Zhao,
Zhengang Zhao
Shanghai University, Shanghai, China
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YangQuan Chen
YangQuan Chen
Utah State University, Logan, UT
Search for other works by this author on:
Changpin Li
Shanghai University, Shanghai, China
Zhengang Zhao
Shanghai University, Shanghai, China
YangQuan Chen
Utah State University, Logan, UT
Paper No:
DETC2009-86693, pp. 1055-1062; 8 pages
Published Online:
July 29, 2010
Citation
Li, C, Zhao, Z, & Chen, Y. "Numerical Approximation and Error Estimation of a Time Fractional Order Diffusion Equation." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C. San Diego, California, USA. August 30–September 2, 2009. pp. 1055-1062. ASME. https://doi.org/10.1115/DETC2009-86693
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