Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697712Issue 3 (Special Issue)20221101A new iteration method for solving space fractional coupled nonlinear Schrödinger equations7047184291010.22067/ijnao.2022.77745.1163ENH. AslaniFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.D. Khojasteh SalkuyehFaculty of Mathematical Sciences, and Center of Excellence for Mathematical Modelling Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran.M. TaghipourFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Journal Article20220717A 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.pdf