On approximating conjugate, focal, and σ-points for linear differential equations of second order
A study of the fundamental nature of solving a system of n ordinary (nondifferential) equations is undertaken in § 1. It is found that the properties of the inverse function play an unexpectedly decisive rôle. In § 2, the results of § 1 are applied to methods of approximating eigenvalues, conjugate, focal, and σ-points previously introduced by the author. Finally, the connection between these methods and Wiman's integral is indicated.
KeywordsDifferential Equation Inverse Function Linear Differential Equation Fundamental Nature
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- W. Leighton,Computing bounds for focal points and for σ-points for second-order linear differential equations, Ordinary Differential Equations, Academic Press, New York (1972).Google Scholar
- A. Wiman,Über die reellen Lösungen der linearen Differentialgleichungen zweiter Ordnung, Arkif für Matematik, Astronomi och Fysik,12 (1917), pp. 1–22.Google Scholar