MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices

In this paper,we devote to improve an effective iterative method for solving weakly nonlinear systems with large sparse complex symmetric Jacobian matrix. Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iteration method for solving linear system with complex symmetric matrix. We propose the Picard-MDSS method based on the separability of linear and nonlinear terms by combining modified DSS (MDSS) methods of linear systems. We explore convergence theorems for the MDSS and Picard-MDSS methods under proper conditions. Furthermore, we conclude that our new methods are more efficient in comparison to several known methods through numerical experiments. The numerical results show the superiority of our new methods in CPU time and iteration steps.