A new iteration method for solving spacefractional coupled nonlinear Schrödingerequations

A linearly implicit difference scheme for the space fractional couplednonlinear schrödinger equation is proposed. the resulting coefficient matrixof the discretized linear system consists of the sum of a complex scaledidentity and a symmetric positive definite, diagonal-plus-toeplitz, matrix.an efficient block gauss–seidel over-relaxation (bgsor) method has beenestablished to solve the discretized linear system. it is worth noting that theproposed method solves the linear equations without the need for any systemsolution, which is beneficial for reducing computational cost and memoryrequirements. theoretical analysis implies that the bgsor method isconvergent under a suitable condition. moreover, an appropriate approachto compute the optimal parameter in the bgsor method is exploited. finally,the theoretical analysis is validated by some numerical experiments.