Summary: Detonation waves have a relevant role in many engineering processes, namely those related to propulsion. Most studies, regarding the stability of detonation waves, have been carried out by computer simulations, notwithstanding their multi-scale nature and unstable behaviour makes it difficult to achieve accurate results. In this paper we propose a kinetic approach to this problem, explain the constraints and the difficulties that this choice entails as well as its advantages. Numerical methods are needed to obtain the solutions of the stability. The ones in use imply that a regular computer takes a long period of time to provide the solutions. In this paper, taking into account the developments proposed by others, we present a numerical procedure that helps to overcome the difficulties of the current methods and allows us to answer some questions related to the stability problem.
For the entire collection see [Zbl 1387.81004].