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

Abstract

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.

Keywords:

• Parabolic reaction–diffusion problem
• Boundary layers
• θ Method
• Monotone iterates
• Uniform convergence

Acknowledgement

The author is very greatful to Dr Matthew Hardy for his help with the implementation of the numerical experiments.