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.