Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives
We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to te...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/540692 |
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| _version_ | 1832564395572461568 |
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| author | Yuxin Zhang Hengfei Ding Jincai Luo |
| author_facet | Yuxin Zhang Hengfei Ding Jincai Luo |
| author_sort | Yuxin Zhang |
| collection | DOAJ |
| description | We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders. |
| format | Article |
| id | doaj-art-2c4b01a09dc4401683e761237f1751ef |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2c4b01a09dc4401683e761237f1751ef2025-02-03T01:11:07ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/540692540692Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz DerivativesYuxin Zhang0Hengfei Ding1Jincai Luo2School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaSchool of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaCaoba Nine-Year School, Honghe Country, Lixian 742203, ChinaWe propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders.http://dx.doi.org/10.1155/2014/540692 |
| spellingShingle | Yuxin Zhang Hengfei Ding Jincai Luo Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives Abstract and Applied Analysis |
| title | Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives |
| title_full | Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives |
| title_fullStr | Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives |
| title_full_unstemmed | Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives |
| title_short | Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives |
| title_sort | fourth order compact difference schemes for the riemann liouville and riesz derivatives |
| url | http://dx.doi.org/10.1155/2014/540692 |
| work_keys_str_mv | AT yuxinzhang fourthordercompactdifferenceschemesfortheriemannliouvilleandrieszderivatives AT hengfeiding fourthordercompactdifferenceschemesfortheriemannliouvilleandrieszderivatives AT jincailuo fourthordercompactdifferenceschemesfortheriemannliouvilleandrieszderivatives |