A monotone weighted average method for a non-linear reaction-diffusion problem

This paper deals with a discrete monotone iterative algorithm for solving a non-linear singularly perturbed parabolic reaction-diffusion problem. The monotone iterative method, which is based on a weighted average difference scheme, is applied to computing a non-linear difference scheme obtained after discretization of the continuous problem. This method solves only linear discrete systems at each iterative step of the iterative process. The uniform convergence of the method is established and numerical experiments are presented.