An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation
In this paper, we solve the space fractional nonlinear Schrödinger equation (SFNSE) by developing an explicit–implicit spectral element scheme, which is formulated based on the Legendre spectral element approximation in space and the Crank–Nicolson leap frog (CNLF) difference discretization in time....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/9/654 |
| _version_ | 1797580056051056640 |
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| author | Zeting Liu Baoli Yin Yang Liu |
| author_facet | Zeting Liu Baoli Yin Yang Liu |
| author_sort | Zeting Liu |
| collection | DOAJ |
| description | In this paper, we solve the space fractional nonlinear Schrödinger equation (SFNSE) by developing an explicit–implicit spectral element scheme, which is formulated based on the Legendre spectral element approximation in space and the Crank–Nicolson leap frog (CNLF) difference discretization in time. Both mass and energy conservative properties are discussed for the spectral element scheme. Numerical stability and convergence of the scheme are proved. Numerical experiments are performed to confirm the high accuracy and efficiency of the proposed numerical scheme. |
| first_indexed | 2024-03-10T22:44:53Z |
| format | Article |
| id | doaj.art-f5a9b2f2ff944ced8ab8aeef9d1d609e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T22:44:53Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f5a9b2f2ff944ced8ab8aeef9d1d609e2023-11-19T10:48:20ZengMDPI AGFractal and Fractional2504-31102023-08-017965410.3390/fractalfract7090654An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger EquationZeting Liu0Baoli Yin1Yang Liu2School of Sports Engineering, Beijing Sport University, Beijing 100084, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaIn this paper, we solve the space fractional nonlinear Schrödinger equation (SFNSE) by developing an explicit–implicit spectral element scheme, which is formulated based on the Legendre spectral element approximation in space and the Crank–Nicolson leap frog (CNLF) difference discretization in time. Both mass and energy conservative properties are discussed for the spectral element scheme. Numerical stability and convergence of the scheme are proved. Numerical experiments are performed to confirm the high accuracy and efficiency of the proposed numerical scheme.https://www.mdpi.com/2504-3110/7/9/654space fractional Schrödinger equationspectral element methodmass and energy conservationstability and convergence |
| spellingShingle | Zeting Liu Baoli Yin Yang Liu An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation Fractal and Fractional space fractional Schrödinger equation spectral element method mass and energy conservation stability and convergence |
| title | An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation |
| title_full | An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation |
| title_fullStr | An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation |
| title_full_unstemmed | An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation |
| title_short | An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation |
| title_sort | explicit implicit spectral element scheme for the nonlinear space fractional schrodinger equation |
| topic | space fractional Schrödinger equation spectral element method mass and energy conservation stability and convergence |
| url | https://www.mdpi.com/2504-3110/7/9/654 |
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