Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle
We are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as well as the 2D case. In order to improve the accuracy of computation we use the precondtitioning strategy for second order differential operator introduced by Labross...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2017-09-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1124 |
| _version_ | 1818529537461321728 |
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| author | Imre Boros |
| author_facet | Imre Boros |
| author_sort | Imre Boros |
| collection | DOAJ |
| description | We are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as well as the 2D case. In order to improve the accuracy of computation we use the precondtitioning strategy for second order differential operator introduced
by Labrosse in 2009. The fourth order differential operator is factorized as a product of second order operators. In order to asses the accuracy of our method we calculate the so called drift of the first five eigenvalues. In both cases ChC method with the considered preconditioners provides accurate eigenpairs of interest. |
| first_indexed | 2024-12-11T17:08:08Z |
| format | Article |
| id | doaj.art-65fce4dbf5c048b2b7778cea30b18b7f |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T17:08:08Z |
| publishDate | 2017-09-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-65fce4dbf5c048b2b7778cea30b18b7f2022-12-22T00:57:37ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2017-09-01461Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangleImre Boros0Tiberiu Popoviciu Institute of Numerical AnalysisWe are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as well as the 2D case. In order to improve the accuracy of computation we use the precondtitioning strategy for second order differential operator introduced by Labrosse in 2009. The fourth order differential operator is factorized as a product of second order operators. In order to asses the accuracy of our method we calculate the so called drift of the first five eigenvalues. In both cases ChC method with the considered preconditioners provides accurate eigenpairs of interest.https://ictp.acad.ro/jnaat/journal/article/view/1124spectral methodsChebyshev collocationpreconditioningfourth order eigenvalue problems |
| spellingShingle | Imre Boros Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle Journal of Numerical Analysis and Approximation Theory spectral methods Chebyshev collocation preconditioning fourth order eigenvalue problems |
| title | Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| title_full | Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| title_fullStr | Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| title_full_unstemmed | Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| title_short | Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| title_sort | accurate chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle |
| topic | spectral methods Chebyshev collocation preconditioning fourth order eigenvalue problems |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1124 |
| work_keys_str_mv | AT imreboros accuratechebyshevcollocationsolutionsforthebiharmoniceigenproblemonarectangle |