An efficient block Gauss–Seidel iteration method for the space fractional coupled nonlinear Schrödinger equations

Abstract

In this paper, we propose an efficient block Gauss–Seidel iteration method for solving the complex linear equations arising from the space fractional coupled nonlinear Schrödinger (CNLS) equations. The proposed method avoids the inverse of coefficient matrix when solving linear equations, which can greatly reduce computation load and storage space. Furthermore, the convergence of the iteration method is proved theoretically and the number of iteration steps is estimated. Numerical results are presented to show the block Gauss–Seidel iteration method can be quite competitive when compared with others.