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We carry out a systematic numerical stability analysis of ZND detonations ofMajda's model with Arrhenius-type ignition function, a simplified model forreacting flow, as heat release and activation energy are varied. Our purposeis, first, to answer a question of Majda whether oscillatory instabilities canoccur for high activation energies as in the full reacting Euler equations,and, second, to test the efficiency of various versions of a numericaleigenvalue-finding scheme suggested by Humpherys and Zumbrun against thestandard method of Lee and Stewart. Our results suggest that instabilities donot occur for Majda's model with Arrhenius-type ignition function, nor with amodified Arrhenius-type ignition function suggested by Lyng--Zumbrun, even inthe high-activation energy limit. We find that the algorithm ofHumpherys--Zumbrun is in the context of Majda's model $100$-$1,000$ timesfaster than the one described in the classical work of Lee and Stewart and$1$-$10$ times faster than an optimized version of the Lee--Stewart algorithmusing an adaptive-mesh ODE solver

A numerical stability investigation of strong ZND detonations for Majda's model