A Spectral Deferred Correction Method for Fractional Differential Equations
A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/139530 |
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| _version_ | 1849306709296676864 |
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| author | Jia Xin Jianfei Huang Weijia Zhao Jiang Zhu |
| author_facet | Jia Xin Jianfei Huang Weijia Zhao Jiang Zhu |
| author_sort | Jia Xin |
| collection | DOAJ |
| description | A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method. |
| format | Article |
| id | doaj-art-2c977ec3afc34ff5877bdab266b5af97 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2c977ec3afc34ff5877bdab266b5af972025-08-20T03:55:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/139530139530A Spectral Deferred Correction Method for Fractional Differential EquationsJia Xin0Jianfei Huang1Weijia Zhao2Jiang Zhu3College of Mathematics, Qingdao University, Qingdao 266071, ChinaCollege of Mathematics, Qingdao University, Qingdao 266071, ChinaCollege of Mathematics, Qingdao University, Qingdao 266071, ChinaNational Laboratory for Scientific Computing, MCTI, Avenida Getulio Vargas 333, 25651-075 Petropolis, RJ, BrazilA spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method.http://dx.doi.org/10.1155/2013/139530 |
| spellingShingle | Jia Xin Jianfei Huang Weijia Zhao Jiang Zhu A Spectral Deferred Correction Method for Fractional Differential Equations Abstract and Applied Analysis |
| title | A Spectral Deferred Correction Method for Fractional Differential Equations |
| title_full | A Spectral Deferred Correction Method for Fractional Differential Equations |
| title_fullStr | A Spectral Deferred Correction Method for Fractional Differential Equations |
| title_full_unstemmed | A Spectral Deferred Correction Method for Fractional Differential Equations |
| title_short | A Spectral Deferred Correction Method for Fractional Differential Equations |
| title_sort | spectral deferred correction method for fractional differential equations |
| url | http://dx.doi.org/10.1155/2013/139530 |
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