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Linear stability of detonation waves is analyzed by means of numerical calculation of time-dependent solutions of linearized Euler equations. No assumption of normal modes is used which helps avoid solving singular systems of ordinary differential equations that arise in normal mode analysis. Here we present the method for the case of one-dimensional flow of an ideal chemically reacting gas with one-step irreversible reaction A → B. Neutral stability boundaries in the plane of heat release vs activation energy are calculated and compared with predictions by normal mode analysis.