Some Features of the Asymptotic-Numerical Method for the Moving Fronts Description in Two-Dimensional Reaction-Diffusion Problems

Abstract

This paper develops an analytic-numerical approach for the description of moving fronts in two-dimensional nonlinear singularly perturbed parabolic equations. Asymptotic technique allows to reduce two-dimensional nonlinear reaction-diffusion equation to a series of more simple one-dimensional problems. This decomposition significantly decreases the complexity of numerical calculations and allows the effective use of parallel computing. Some numerical experiments are presented to demonstrate the main features of the proposed method.