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A Numerical Method for the Solution of the Time-Fractional Diffusion Equation

Title
A Numerical Method for the Solution of the Time-Fractional Diffusion Equation
Type
Article in International Conference Proceedings Book
Year
2014
Authors
Ferras, LL
(Author)
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Ford, NJ
(Author)
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Morgado, ML
(Author)
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Rebelo, M
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Conference proceedings International
Pages: 117-131
14th International Conference on Computational Science and Its Applications (ICCSA)
Guimaraes, PORTUGAL, JUN 30-JUL 03, 2014
Other information
Authenticus ID: P-009-Q5C
Abstract (EN): In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.
Language: English
Type (Professor's evaluation): Scientific
No. of pages: 15
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