  We numerically calculate the quasinormal frequencies of the Klein-Gordon and
Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter
black hole of the dilaton gravity theory. For the Klein-Gordon field we use the
Horowitz-Hubeny method and the asymptotic iteration method for second order
differential equations. For the Dirac field we first exploit the
Horowitz-Hubeny method. As a second method, instead of using the asymptotic
iteration method for second order differential equations, we propose to take as
a basis its formulation for coupled systems of first order differential
equations. For the two fields we find that the results that produce the two
numerical methods are consistent. Furthermore for both fields we obtain that
their quasinormal modes are stable and we compare their quasinormal frequencies
to analyze whether their spectra are isospectral. Finally we discuss the main
results.
