We carry out a systematic numerical stability analysis of ZND detonations of
Majda's model with Arrhenius-type ignition function, a simplified model for
reacting flow, as heat release and activation energy are varied. Our purpose
is, first, to answer a question of Majda whether oscillatory instabilities can
occur for high activation energies as in the full reacting Euler equations,
and, second, to test the efficiency of various versions of a numerical
eigenvalue-finding scheme suggested by Humpherys and Zumbrun against the
standard method of Lee and Stewart.