  We perform error analyses explaining some previously mysterious phenomena
arising in numerical computation of the Evans function, in particular (i) the
advantage of centered coordinates for exterior product and related methods, and
(ii) the unexpected stability of the (notoriously unstable) continuous
orthogonalization method of Drury in the context of Evans function
applications. The analysis in both cases centers around a numerical version of
the gap lemma of Gardner--Zumbrun and Kapitula--Sandstede, giving uniform error
estimates for apparently ill-posed projective boundary-value problems with
asymptotically constant coefficients, so long as the rate of convergence of
coefficients is greater than the "badness" of the boundary projections as
measured by negative spectral gap. In the second case, we use also the simple
but apparently previously unremarked observation that the Drury method is in
fact (neutrally) stable when used to approximate an unstable subspace, so that
continuous orthogonalization and the centered exterior product method are
roughly equally well-conditioned as methods for Evans function approximation.
The latter observation makes possible an extremely simple nonlinear
boundary-value method for possible use in large-scale systems, extending ideas
suggested by Sandstede. We suggest also a related linear method based on the
conjugation lemma of M\'etivier--Zumbrun, an extension of the gap lemma
mentioned above.
