MONOTONE ITERATIVE SCHEME FOR WEAKLY COUPLED SYSTEM OF FINITE DIFFERENCE REACTION-DIFFUSION EQUATIONS

摘要

The purpose of this paper is to develop monotone iteration scheme using the notion of upper and lower solutions for system of nonlinear finite difference equations, which correspond to the weakly coupled system of nonlinear reaction-diffusion equations with nonlinear boundary conditions. Two monotone sequences are constructed for the finite difference equations when both reaction function and boundary function are mixed quasimonotone. It is shown that these sequences converge monotonically to a solution of the finite difference system, which leads to existence-comparison result for the solution of the problem.