  We introduce a new method to investigate linear stability of gaseous
detonations that is based on an accurate shock-fitting numerical integration of
the linearized reactive Euler equations with a subsequent analysis of the
computed solution via the dynamic mode decomposition. The method is applied to
the detonation models based on both the standard one-step Arrhenius kinetics
and two-step exothermic-endothermic reaction kinetics. Stability spectra for
all cases are computed and analyzed. The new approach is shown to be a viable
alternative to the traditional normal-mode analysis used in detonation theory.
