Abstract
The aim of this paper is to develop monotone iterative scheme using the notion of upper-lower solutions for weakly coupled system of finite difference equations which corresponds to weakly coupled system of semilinear time degenerate parabolic Dirichlet initial boundary value problem (IBVP). Using upper and lower solutions as distinct initial iterations, two monotone convergent sequences from linear system are constructed. It is shown that these two sequences converge monotonically from above and below to maximal and minimal solutions respectively which lead to the existence-comparison and uniqueness results for the solution of the discrete nonlinear Dirichlet IBVP. Positivity lemma is the main ingredient used in the proof of these results. AMS Subject Classification: 65Q10
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