  We modify the freezing method introduced by Beyn & Thuemmler, 2004, for
analyzing rigidly rotating spiral waves in excitable media. The proposed method
is designed to stably determine the rotation frequency and the core radius of
rotating spirals, as well as the approximate shape of spiral waves in unbounded
domains. In particular, we introduce spiral wave boundary conditions based on
geometric approximations of spiral wave solutions by Archimedean spirals and by
involutes of circles. We further propose a simple implementation of boundary
conditions for the case when the inhibitor is non-diffusive, a case which had
previously caused spurious oscillations.
  We then utilize the method to numerically analyze the large core limit. The
proposed method allows us to investigate the case close to criticality where
spiral waves acquire infinite core radius and zero rotation frequency, before
they begin to develop into retracting fingers. We confirm the linear scaling
regime of a drift bifurcation for the rotation frequency and the core radius of
spiral wave solutions close to criticality. This regime is unattainable with
conventional numerical methods.
