Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction–diffusion problem

Abstract

A new approach to the numerical simulation of the reaction front motion in a nonlinear singularly perturbed partial differential equation of the reaction–diffusion type is proposed. It is shown how the methods of asymptotic analysis allow reducing the statement of the original problem to a problem of a smaller dimension, the numerical solving of which uses methods of diagnostics of the solution’s blow-up. Numerical experiments demonstrate the effectiveness of the proposed approach.