  We demonstrate a geometrically inspired technique for computing Evans
functions for the linearised operators about travelling waves. Using the
examples of the F-KPP equation and a Keller-Segel model of bacterial
chemotaxis, we produce an Evans function which is computable through several
orders of magnitude in the spectral parameter and show how such a function can
naturally be extended into the continuous spectrum. In both examples, we use
this function to numerically verify the absence of eigenvalues in a large
region of the right half of the spectral plane. We also include a new proof of
spectral stability in the appropriate weighted space of travelling waves of
speed $c \geq 2 \sqrt{\delta}$ in the F-KPP equation.
