Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations
Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on Legendre Galerkin formulation while the Cheby...
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| Main Authors: | , , , , , |
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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/10.1155/2012/106343 |
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| author | Tinggang Zhao Xiaoxian Zhang Jinxia Huo Wanghui Su Yongli Liu Yujiang Wu |
| author_facet | Tinggang Zhao Xiaoxian Zhang Jinxia Huo Wanghui Su Yongli Liu Yujiang Wu |
| author_sort | Tinggang Zhao |
| collection | DOAJ |
| description | Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. Optimal error estimate of the Chebyshev-Legendre method is proved for the problem with Dirichlet boundary condition. The convergence rate shows “spectral accuracy.” Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results. |
| format | Article |
| id | doaj-art-c999495b8a7e4c24be238bea5d97eb9a |
| 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-c999495b8a7e4c24be238bea5d97eb9a2025-02-03T01:07:18ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/106343106343Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers EquationsTinggang Zhao0Xiaoxian Zhang1Jinxia Huo2Wanghui Su3Yongli Liu4Yujiang Wu5School of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaCombining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. Optimal error estimate of the Chebyshev-Legendre method is proved for the problem with Dirichlet boundary condition. The convergence rate shows “spectral accuracy.” Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.http://dx.doi.org/10.1155/2012/106343 |
| spellingShingle | Tinggang Zhao Xiaoxian Zhang Jinxia Huo Wanghui Su Yongli Liu Yujiang Wu Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations Abstract and Applied Analysis |
| title | Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations |
| title_full | Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations |
| title_fullStr | Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations |
| title_full_unstemmed | Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations |
| title_short | Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations |
| title_sort | optimal error estimate of chebyshev legendre spectral method for the generalised benjamin bona mahony burgers equations |
| url | http://dx.doi.org/10.1155/2012/106343 |
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