Abstract
This paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method. Three monotone iteration processes for the finite difference system are presented, and the sequences of iterations are shown to converge monotonically to a unique solution of the system, including an existence-uniqueness-comparison theorem. A theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given. Also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary-value problem. An application to a reaction-diffusion model in chemical engineering and combustion theory is given.
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