Approximate solutions to singular perturbation problems: The intermediate variable technique

Abstract

The intermediate variable technique, developed by S. Kaplun, “Fluid Mechanics and Singular Perturbations,” Academic Press, San Diego, 1967, and by P. A. Lagerstrom and R. G. Casten, Basic concepts underlying singular perturbation techniques, SIAM Rev. 14 (1972), 63–120, for the solution of singular perturbation problems, is applied to several problems which are normally solved by other perturbative methods. The objective of the present analysis is to obtain approximate solutions which are characterized by their domains of validity, so that the matching of adjacent solutions is promptly determined. The analysis also shows how the intermediate equations can be derived and how they play an important role in the determination of approximate Solutions.