Monotone finite difference schemes for nonlinear systems with mixed quasi-monotonicity

Monotone finite difference schemes are proposed for nonlinear systems with mixed quasi-monotonicity. Two monotone iteration processes for the corresponding discrete problems are presented, which converge monotonically to the quasi-solutions of the discrete problems. The limits are the exact solutions under some conditions. A monotone finite difference scheme on uniform mesh with the accuracy of fourth order is constructed. The numerical results coincide with theoretical analysis.