SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations
In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022049?viewType=HTML |
| _version_ | 1811251249079648256 |
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| author | Chunye Gong Mianfu She Wanqiu Yuan Dan Zhao |
| author_facet | Chunye Gong Mianfu She Wanqiu Yuan Dan Zhao |
| author_sort | Chunye Gong |
| collection | DOAJ |
| description | In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete scheme is proved to be mass- and energy- conserved. Moreover, unconditional energy stability and convergence of the scheme are obtained by the use of the Gagliardo-Nirenberg and some Sobolev inequalities. Numerical results are presented to confirm our theoretical findings. |
| first_indexed | 2024-04-12T16:16:53Z |
| format | Article |
| id | doaj.art-d90d7962d9234ae484e87f46dee3e449 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T16:16:53Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-d90d7962d9234ae484e87f46dee3e4492022-12-22T03:25:42ZengAIMS PressElectronic Research Archive2688-15942022-03-0130394396010.3934/era.2022049SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equationsChunye Gong0Mianfu She1Wanqiu Yuan2 Dan Zhao31. School of Computer Science, National University of Defense Technology, Changsha 410073, China2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaIn this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete scheme is proved to be mass- and energy- conserved. Moreover, unconditional energy stability and convergence of the scheme are obtained by the use of the Gagliardo-Nirenberg and some Sobolev inequalities. Numerical results are presented to confirm our theoretical findings.https://www.aimspress.com/article/doi/10.3934/era.2022049?viewType=HTMLnonlinear schrödinger-possion equationsenergy stabilityerror estimatesgalerkin-legendre spectral methodscalar auxiliary variable (sav) |
| spellingShingle | Chunye Gong Mianfu She Wanqiu Yuan Dan Zhao SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations Electronic Research Archive nonlinear schrödinger-possion equations energy stability error estimates galerkin-legendre spectral method scalar auxiliary variable (sav) |
| title | SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations |
| title_full | SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations |
| title_fullStr | SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations |
| title_full_unstemmed | SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations |
| title_short | SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations |
| title_sort | sav galerkin legendre spectral method for the nonlinear schrodinger possion equations |
| topic | nonlinear schrödinger-possion equations energy stability error estimates galerkin-legendre spectral method scalar auxiliary variable (sav) |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022049?viewType=HTML |
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