Abstract: This paper studied the finite difference solutions of a cooperative model with diffusion. A monotone iterative scheme was developed for solving the nonlinear finite difference system. The existence and uniqueness of a nonnegative solution was investigated. It was shown that the system may have four types of
nonnegative solutions for different parameters, and each of these solutions could be computed by a suitable choice of initial iteration in the monotone iterative scheme. Some numerical results were given.

Key words: cooperative model, finite difference system, nonnegative solution, monotone iteration  ,