Abstract
AbstractIn this article we study a finite‐difference system, which is a discrete version of a class of nonlinear reaction‐diffusion systems with time delays. Existence‐comparison and uniqueness theorem are first established for the discretized problem by the method of upper and lower solutions. A monotone iterative scheme is also developed for the solution of the finite‐difference system. Under a convergence acceleration scheme, it is shown that the monotone sequences converge quadratically to the solution of the finite‐difference system. At last, numerical results on some model problems are demonstrated to substantiate our theorems. © 1995 John Wiley & Sons, Inc.
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