A new iteration method for solving space fractional coupled nonlinear Schrödinger equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 11، دوره 12، Issue 3 (Special Issue) - شماره پیاپی 23، بهمن 2022، صفحه 704-718   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.77745.1163

نویسندگان

H. Aslani¹؛ D. Khojasteh Salkuyeh^{* 2}؛ M. Taghipour¹

¹Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

²Faculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.

چکیده

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.

کلیدواژه‌ها

The space fractional Schrödinger equations؛ Toeplitz matrix؛ Block Gauss-Seidel over-relaxation method؛ Convergence analysis

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