High-Order Algorithms for Riesz Derivative and Their Applications (I)
We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/653797 |
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| Summary: | We firstly develop the high-order numerical algorithms for
the left and right Riemann-Liouville derivatives. Using these derived schemes,
we can get high-order algorithms for the Riesz fractional derivative. Based on
the approximate algorithm, we construct the numerical scheme for the space
Riesz fractional diffusion equation, where a fourth-order scheme is proposed
for the spacial Riesz derivative, and where a compact difference scheme is
applied to approximating the first-order time derivative. It is shown that the
difference scheme is unconditionally stable and convergent. Finally, numerical
examples are provided which are in line with the theoretical analysis. |
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| ISSN: | 1085-3375 1687-0409 |