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 so-lutions 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 ap-proach. As an illustration, we shall apply the above methods to an autocatalytic reaction involving two diffusing chemi-cals in one spatial dimension. Prospects of further work are also discussed.