Stability of idealized one-reaction detonations revisited

It is shown that the discrete spectrum stemming from the solution of the initial-value problem for an idealized one-reaction detonation is equivalent to the spectrum of the conventional normal-mode approach. Solution of the initial-value problem also leads to a method for expanding the perturbation field into modes of discrete and continuous spectra. In addition, it gives a convenient tool to predict initial amplitudes of the unstable modes depending on the initial perturbation. A multi-domain spectral collocation method is utilized for analysis of the discrete spectrum. The method provides an efficient tool for computation of the eigenvalue map in studies of the stability of detonations.