  A computational linear stability analysis of spiral waves in a
reaction-diffusion equation is performed on large disks. As the disk radius R
increases, eigenvalue spectra converge to the absolute spectrum predicted by
Sandstede and Scheel. The convergence rate is consistent with 1/R, except
possibly near the edge of the spectrum. Eigenfunctions computed on large disks
are compared with predicted exponential forms. Away from the edge of the
absolute spectrum the agreement is excellent, while near the edge computed
eigenfunctions deviate from predictions, probably due to finite-size effects.
In addition to eigenvalues associated with the absolute spectrum, computations
reveal point eigenvalues. The point eigenvalues and associated eigenfunctions
responsible for both core and far-field breakup of spiral waves are shown.
