A new iteration method for solving space fractional coupled nonlinear Schrödinger equations
A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive definite, diagonal-plus-Toeplitz, matrix. An e...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2022-11-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_42910_a05473d0466ef87ea4c35bbdbc7461d8.pdf |
| _version_ | 1798018862984200192 |
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| author | H. Aslani D. Khojasteh Salkuyeh M. Taghipour |
| author_facet | H. Aslani D. Khojasteh Salkuyeh M. Taghipour |
| author_sort | H. Aslani |
| collection | DOAJ |
| description | A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive definite, diagonal-plus-Toeplitz, matrix. An efficient block Gauss–Seidel over-relaxation (BGSOR) method has been established to solve the discretized linear system. It is worth noting that the proposed method solves the linear equations without the need for any system solution, which is beneficial for reducing computational cost and memory requirements. Theoretical analysis implies that the BGSOR method is convergent under a suitable condition. Moreover, an appropriate approach to compute the optimal parameter in the BGSOR method is exploited. Finally, the theoretical analysis is validated by some numerical experiments. |
| first_indexed | 2024-04-11T16:31:13Z |
| format | Article |
| id | doaj.art-36fef8a45b8544c19916dd5006a460e3 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-04-11T16:31:13Z |
| publishDate | 2022-11-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-36fef8a45b8544c19916dd5006a460e32022-12-22T04:14:01ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692022-11-0112Issue 3 (Special Issue) - On the occasion of the 75th birthday of Professor A. Vahidian and Professor F. Toutounian70471810.22067/ijnao.2022.77745.116342910A new iteration method for solving space fractional coupled nonlinear Schrödinger equationsH. Aslani0D. Khojasteh Salkuyeh1M. Taghipour2Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Faculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive definite, diagonal-plus-Toeplitz, matrix. An efficient block Gauss–Seidel over-relaxation (BGSOR) method has been established to solve the discretized linear system. It is worth noting that the proposed method solves the linear equations without the need for any system solution, which is beneficial for reducing computational cost and memory requirements. Theoretical analysis implies that the BGSOR method is convergent under a suitable condition. Moreover, an appropriate approach to compute the optimal parameter in the BGSOR method is exploited. Finally, the theoretical analysis is validated by some numerical experiments.https://ijnao.um.ac.ir/article_42910_a05473d0466ef87ea4c35bbdbc7461d8.pdfthe space fractional schrödinger equationstoeplitz matrixblock gauss-seidel over-relaxation methodconvergence analysis |
| spellingShingle | H. Aslani D. Khojasteh Salkuyeh M. Taghipour A new iteration method for solving space fractional coupled nonlinear Schrödinger equations Iranian Journal of Numerical Analysis and Optimization the space fractional schrödinger equations toeplitz matrix block gauss-seidel over-relaxation method convergence analysis |
| title | A new iteration method for solving space fractional coupled nonlinear Schrödinger equations |
| title_full | A new iteration method for solving space fractional coupled nonlinear Schrödinger equations |
| title_fullStr | A new iteration method for solving space fractional coupled nonlinear Schrödinger equations |
| title_full_unstemmed | A new iteration method for solving space fractional coupled nonlinear Schrödinger equations |
| title_short | A new iteration method for solving space fractional coupled nonlinear Schrödinger equations |
| title_sort | new iteration method for solving space fractional coupled nonlinear schrodinger equations |
| topic | the space fractional schrödinger equations toeplitz matrix block gauss-seidel over-relaxation method convergence analysis |
| url | https://ijnao.um.ac.ir/article_42910_a05473d0466ef87ea4c35bbdbc7461d8.pdf |
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