An Analysis of the Time-Dependent Neutron Transport Equation with Delayed Neutrons by the Method of Matched Asymptotic Expansions

The time-dependent neutron transport equation is treated as a problem in singular perturbation theory. The method of matched asymptotic expansions is used to find equations yielding approximate solutions that are uniformly valid in time. The long-time solutions resulting from this method are those of the prompt-jump approximation. Although best suited for fast subcritical systems, numerical results from diffusion theory calculations indicate that very good accuracy is obtained for thermal systems as well.