A Generalized Method for Treating Singular Perturbation Problems

摘要

Some of the existing methods of treating singular perturbation problems are studied, and a generalized method for solving such problems is developed. The generalized method was applied to a restricted three-body problem and to a general second-order linear ordinary differential equation with a turning point of arbitrary order. The results of the latter are used in obtaining the asymptotic expansions of the eigenvalues and eigenfunctions of a second-order linear equation with two turning points of arbitrary order. A special case of the eigenvalue problem is the Graetz problem. It arises in finding the temperature distribution of a fluid with constant properties having a parabolic velocity profile which enters suddenly into a round tube whose wall is kept at a different constant temperature. (Author)