Numerical methods for the travelling wave solutions in reaction-diffusion equations

Abstract

In this work we consider how shooting and relaxation methods can be used to investigate propagating waves solutions of PDEs. Particular attention is paid to overcoming some of the numerical difficulties. The linear stability of these solutions are analyzed by using the Evans function approach. As an illustration, we shall apply the above methods to an autocatalytic reaction involving two diffusing chemicals in one spatial dimension. Prospects of further work are also discussed.