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...
| Main Authors: | , , |
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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 |
| Summary: | 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. |
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| ISSN: | 2423-6977 2423-6969 |