Abstract
In this paper we consider the application of additive operator splitting methods for solving a finite difference nonlinear system of the form F ( u ) = ( I − τA( u )) u − w = 0 generated by the discretization of two dimensional diffusion–convection problems with Neumann boundary conditions. Existence and uniqueness of a solution of this system has been proved under standard assumptions on the matrix A( u ) and the source term w . Using the fact that the matrix A( u ) can be decomposed into different splittings, we develop a nonlinear Arithmetic Mean method and a two-stage iterative method (a fixed-point-Arithmetic Mean method) for solving the system above. The convergence of these methods has been analyzed. Numerical experiments show that the fixed-point-Arithmetic Mean method is rapidly convergent when the diffusion coefficient is weakly nonlinear.
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