Parallel multisplitting methods for a class of systems of weakly nonlinear equations without isotone mapping

A parallel matrix multisplitting iterative method is set up for a class of systems of weakly nonlinear equations without isotone mapping. The two-sided monotone convergence is shown. A sufficient condition is given to ensure the monotone convergence of the new method to the unique solution of the system in some sector. The influences of different multisplittings on the convergence rate are investigated in the sense of monotonicity. A numerical example is given.