A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods
We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differentia...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/603748 |
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| _version_ | 1832562198354853888 |
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| author | F. Z. Geng X. M. Li |
| author_facet | F. Z. Geng X. M. Li |
| author_sort | F. Z. Geng |
| collection | DOAJ |
| description | We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective. |
| format | Article |
| id | doaj-art-8506135c1e644ba89640f81e3553542c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8506135c1e644ba89640f81e3553542c2025-02-03T01:23:17ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/603748603748A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization MethodsF. Z. Geng0X. M. Li1Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, ChinaDepartment of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, ChinaWe introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.http://dx.doi.org/10.1155/2012/603748 |
| spellingShingle | F. Z. Geng X. M. Li A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods Abstract and Applied Analysis |
| title | A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods |
| title_full | A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods |
| title_fullStr | A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods |
| title_full_unstemmed | A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods |
| title_short | A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods |
| title_sort | new method for riccati differential equations based on reproducing kernel and quasilinearization methods |
| url | http://dx.doi.org/10.1155/2012/603748 |
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