Monotone Iterative Method for Weakly Coupled System of Finite Difference Degenerate Parabolic Equations with Mixed Monotonicity Condition.

The purpose of this paper is to present an existence-comparison and uniqueness theorem as well as an iterative method for finite difference system, which correspond to a class of semilinear weakly coupled system of time degenerate parabolic initial boundary value problems. The basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and construction of monotone sequences from a suitable linear discrete system. Using upper and lower solutions as two distinct initial iterations, two monotone sequences are constructed from a suitable linear system under mixed quasimonotonicity condition. It is shown that these sequences converge monotonically to a solution of the discrete system. [ABSTRACT FROM AUTHOR]