A note on Asymptotic Methods for Jump Phenomena

Traditional singular perturbation methods are employed to develop a solution to a differential equation considered by Reiss [SIAM J. Appl. Math., 39 (1980), pp. 440–455] which models an elementary chemical process. The results are compared with those found by Reiss, who used a novel asymptotic method to construct solutions which exhibit rapid transient behavior. It is shown that Reiss’ jump solution corresponds to the asymptotic (large time) representation of the more complete solution found from a formal matched asymptotic expansion procedure. A comparison of results in the rapid transition region obtained from the exact solution, from those found by Reiss and from the matched asymptotic expansion solution developed here, show that the last is far more accurate than the second.