Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs
We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/705179 |
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| _version_ | 1832552822841802752 |
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| author | Cuicui Liao Xiaohua Ding |
| author_facet | Cuicui Liao Xiaohua Ding |
| author_sort | Cuicui Liao |
| collection | DOAJ |
| description | We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle
discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments. |
| format | Article |
| id | doaj-art-03e4c6233abb4e88b715ab0e53946026 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-03e4c6233abb4e88b715ab0e539460262025-02-03T05:57:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/705179705179Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEsCuicui Liao0Xiaohua Ding1Department of Mathematics, Harbin Institute of Technology, 2 Wenhua West Road, Shandong, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology, 2 Wenhua West Road, Shandong, Weihai 264209, ChinaWe use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments.http://dx.doi.org/10.1155/2012/705179 |
| spellingShingle | Cuicui Liao Xiaohua Ding Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs Journal of Applied Mathematics |
| title | Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs |
| title_full | Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs |
| title_fullStr | Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs |
| title_full_unstemmed | Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs |
| title_short | Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs |
| title_sort | nonstandard finite difference variational integrators for multisymplectic pdes |
| url | http://dx.doi.org/10.1155/2012/705179 |
| work_keys_str_mv | AT cuicuiliao nonstandardfinitedifferencevariationalintegratorsformultisymplecticpdes AT xiaohuading nonstandardfinitedifferencevariationalintegratorsformultisymplecticpdes |