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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| _version_ | 1850175280790896640 |
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| author | Hengfei Ding Changpin Li YangQuan Chen |
| author_facet | Hengfei Ding Changpin Li YangQuan Chen |
| author_sort | Hengfei Ding |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ce892ce6ac7840deb5f5384930fa22f7 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ce892ce6ac7840deb5f5384930fa22f72025-08-20T02:19:30ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/653797653797High-Order Algorithms for Riesz Derivative and Their Applications (I)Hengfei Ding0Changpin Li1YangQuan Chen2Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Engineering, University of California, Merced, CA 95343, USAWe 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.http://dx.doi.org/10.1155/2014/653797 |
| spellingShingle | Hengfei Ding Changpin Li YangQuan Chen High-Order Algorithms for Riesz Derivative and Their Applications (I) Abstract and Applied Analysis |
| title | High-Order Algorithms for Riesz Derivative and Their Applications (I) |
| title_full | High-Order Algorithms for Riesz Derivative and Their Applications (I) |
| title_fullStr | High-Order Algorithms for Riesz Derivative and Their Applications (I) |
| title_full_unstemmed | High-Order Algorithms for Riesz Derivative and Their Applications (I) |
| title_short | High-Order Algorithms for Riesz Derivative and Their Applications (I) |
| title_sort | high order algorithms for riesz derivative and their applications i |
| url | http://dx.doi.org/10.1155/2014/653797 |
| work_keys_str_mv | AT hengfeiding highorderalgorithmsforrieszderivativeandtheirapplicationsi AT changpinli highorderalgorithmsforrieszderivativeandtheirapplicationsi AT yangquanchen highorderalgorithmsforrieszderivativeandtheirapplicationsi |