Fourier Spectral Method for a Class of Nonlinear Schrödinger Models
In this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9934858 |
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| _version_ | 1832561423400566784 |
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| author | Lei Zhang Weihua Ou Yang Xuan Liu Haidong Qu |
| author_facet | Lei Zhang Weihua Ou Yang Xuan Liu Haidong Qu |
| author_sort | Lei Zhang |
| collection | DOAJ |
| description | In this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential time-differencing Runge-Kutta method is used to discrete temporal direction. The proof of the conservation law of the mass and the energy for the semidiscrete and full-discrete Fourier spectral scheme is given. The error of the semidiscrete Fourier spectral scheme is analyzed in the proper Sobolev space. Finally, several numerical examples are presented to support our analysis. |
| format | Article |
| id | doaj-art-4bb0d3e1427a4c6bb672e031d3b74d58 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-4bb0d3e1427a4c6bb672e031d3b74d582025-02-03T01:24:59ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/99348589934858Fourier Spectral Method for a Class of Nonlinear Schrödinger ModelsLei Zhang0Weihua Ou Yang1Xuan Liu2Haidong Qu3Department of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaIn this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential time-differencing Runge-Kutta method is used to discrete temporal direction. The proof of the conservation law of the mass and the energy for the semidiscrete and full-discrete Fourier spectral scheme is given. The error of the semidiscrete Fourier spectral scheme is analyzed in the proper Sobolev space. Finally, several numerical examples are presented to support our analysis.http://dx.doi.org/10.1155/2021/9934858 |
| spellingShingle | Lei Zhang Weihua Ou Yang Xuan Liu Haidong Qu Fourier Spectral Method for a Class of Nonlinear Schrödinger Models Advances in Mathematical Physics |
| title | Fourier Spectral Method for a Class of Nonlinear Schrödinger Models |
| title_full | Fourier Spectral Method for a Class of Nonlinear Schrödinger Models |
| title_fullStr | Fourier Spectral Method for a Class of Nonlinear Schrödinger Models |
| title_full_unstemmed | Fourier Spectral Method for a Class of Nonlinear Schrödinger Models |
| title_short | Fourier Spectral Method for a Class of Nonlinear Schrödinger Models |
| title_sort | fourier spectral method for a class of nonlinear schrodinger models |
| url | http://dx.doi.org/10.1155/2021/9934858 |
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