Isospectral heterogeneous domains: A numerical study

We have applied the finite differences method to the study of a pair of isospectral heterogeneous domains, first introduced in Ref. [1]. We show that Richardson and Padé-Richardson extrapolations can be used (as in the homogeneous case) to obtain very precise approximations to the lowest eigenvalues. We have found that the first few exponents of the asymptotic series for the finite difference eigenvalues are unchanged with from the homogeneous case. Additionally, we have improved the previous best estimates for the case of homogeneous isospectral domains, obtaining 10 extra correct digits for the fundamental mode (and similar results for the other eigenvalues), with respect to the best result previously available.