Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem
A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a represent...
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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/10.1155/2014/630671 |
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| _version_ | 1832555875479322624 |
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| author | Jing Niu Ping Li |
| author_facet | Jing Niu Ping Li |
| author_sort | Jing Niu |
| collection | DOAJ |
| description | A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. Moreover, the uniform convergency is proved and the effectiveness of the proposed method is illustrated with some examples. |
| format | Article |
| id | doaj-art-af02849e0874495eb644944bb8b5e994 |
| 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-af02849e0874495eb644944bb8b5e9942025-02-03T05:46:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/630671630671Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value ProblemJing Niu0Ping Li1School of Mathematics and Sciences, Harbin Normal University, Harbin 150025, ChinaSchool of Mathematics and Sciences, Harbin Normal University, Harbin 150025, ChinaA numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. Moreover, the uniform convergency is proved and the effectiveness of the proposed method is illustrated with some examples.http://dx.doi.org/10.1155/2014/630671 |
| spellingShingle | Jing Niu Ping Li Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem Abstract and Applied Analysis |
| title | Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem |
| title_full | Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem |
| title_fullStr | Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem |
| title_full_unstemmed | Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem |
| title_short | Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem |
| title_sort | numerical algorithm for the third order partial differential equation with three point boundary value problem |
| url | http://dx.doi.org/10.1155/2014/630671 |
| work_keys_str_mv | AT jingniu numericalalgorithmforthethirdorderpartialdifferentialequationwiththreepointboundaryvalueproblem AT pingli numericalalgorithmforthethirdorderpartialdifferentialequationwiththreepointboundaryvalueproblem |