  The Evans function has been used extensively to study spectral stability of
travelling-wave solutions in spatially extended partial differential equations.
To compute Evans functions numerically, several shooting methods have been
developed. In this paper, an alternative scheme for the numerical computation
of Evans functions is presented that relies on an appropriate boundary-value
problem formulation. Convergence of the algorithm is proved, and several
examples, including the computation of eigenvalues for a multi-dimensional
problem, are given. The main advantage of the scheme proposed here compared
with earlier methods is that the scheme is linear and scalable to large
problems.
