Solving a singular DAE model of unconfined detonation

We consider a simplified model of an unconfined one-dimensional detonation problem, giving a brief survey of the history of the problem and of its num erical solution. This problem with its mathematical features is typical of those solved commercially by ICI pie, and the specific values used for the chemical constants in the example are typical of those of interest. Unfortu nately, not all obvious methods work well, because of the singular nature o f the problem at the Chapman-Jouguet shock front. We concentrate on shootin g methods for the detonation problem based on backward differentiation form ula integrators, and present a new analysis which explains how these method s work. Finally, we outline some possibilities for further work, including discussing a more general detonation-problem, previous solutions and potent ial future solution methods. (C) 2001 Elsevier Science Ltd. All rights rese rved.