A generalized method for treating singular perturbation problems

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Dept. of Aeronautics and Astronautics, 1964 - Perturbation (Mathematics) - 55 pages
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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).

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Contents

Chapter Page
1
A Restricted ThreeBody Problem
21
SecondOrder Linear Differntial Equations with Turning
33
B Equations with regular singular points
43
Bibliography
55

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