Reproducing kernel methods for solving linear initial-boundary-value problems
In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2008-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/29/abstr.html |
| _version_ | 1819210697912877056 |
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| author | Li-Hong Yang Yingzhen Lin |
| author_facet | Li-Hong Yang Yingzhen Lin |
| author_sort | Li-Hong Yang |
| collection | DOAJ |
| description | In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the sense of the space norm, and a numerical example is given to illustrate the method. |
| first_indexed | 2024-12-23T06:15:18Z |
| format | Article |
| id | doaj.art-9f56d74ff5fc4c0281485966f8dc9a0e |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T06:15:18Z |
| publishDate | 2008-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-9f56d74ff5fc4c0281485966f8dc9a0e2022-12-21T17:57:19ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912008-02-01200829111Reproducing kernel methods for solving linear initial-boundary-value problemsLi-Hong YangYingzhen LinIn this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the sense of the space norm, and a numerical example is given to illustrate the method.http://ejde.math.txstate.edu/Volumes/2008/29/abstr.htmlHyperbolic equationlinear initial-boundary conditionsreproducing kernel space |
| spellingShingle | Li-Hong Yang Yingzhen Lin Reproducing kernel methods for solving linear initial-boundary-value problems Electronic Journal of Differential Equations Hyperbolic equation linear initial-boundary conditions reproducing kernel space |
| title | Reproducing kernel methods for solving linear initial-boundary-value problems |
| title_full | Reproducing kernel methods for solving linear initial-boundary-value problems |
| title_fullStr | Reproducing kernel methods for solving linear initial-boundary-value problems |
| title_full_unstemmed | Reproducing kernel methods for solving linear initial-boundary-value problems |
| title_short | Reproducing kernel methods for solving linear initial-boundary-value problems |
| title_sort | reproducing kernel methods for solving linear initial boundary value problems |
| topic | Hyperbolic equation linear initial-boundary conditions reproducing kernel space |
| url | http://ejde.math.txstate.edu/Volumes/2008/29/abstr.html |
| work_keys_str_mv | AT lihongyang reproducingkernelmethodsforsolvinglinearinitialboundaryvalueproblems AT yingzhenlin reproducingkernelmethodsforsolvinglinearinitialboundaryvalueproblems |