**Stability of travelling-waves to a system of reaction diffusion
equations modelling an autocatalytic chemical reaction**

I will introduce the use of the Evans function for
determining the structure of the spectrum and hence
stability of steady solutions to equations modelling
autocatalytic chemical reactions. I'll outline the
computational complexities that typically arise and survey
methods that have been developed to overcome these.
Finally, I will speak about efficient algorithms that have
been recently developed and which considerably reduce the
compuational time needed to construct the Evans
function. These new algorithms use the Neumann and Magnus
expansion solutions to systems of nonautonomous linear
ordinary differential equations.

*Simon Malham*