A two-stage iterative method for solving weakly nonlinear systems

In this paper we consider a two-stage iterative method for solving weakly nonlinear systems generated by the discretization of semilinear elliptic boundary value problems. This method is well suited for implementation on parallel computers. Theorems about the convergence and the monotone convergence of the method are proved. An application of the method for solving real practical problems related to the study of reaction-diffusion processes and of interacting populations is described.