On SOR-like iteration methods for solving weakly nonlinear systems

In this paper, we introduce a class of SOR-like iteration methods for solving the systems of the weakly nonlinear equation, which is by reformulating equivalently the weakly nonlinear equation as a two-by-two block nonlinear equation. Two types of the global convergence theorems are given under suitable choices of the involved splitting matrix and parameter. Numerical results for the three-dimensional nonlinear convection-diffusion equation and the linear complementarity problem show that the proposed iteration methods are feasible and efficient for solving the weakly nonlinear equations.