Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T02:00:36.862Z Has data issue: false hasContentIssue false
  • English
  • Français

Langer's method for a second order linear ordinary differential equation with a double pole

Published online by Cambridge University Press:  24 October 2008

Donatus Uzodinma Anyanwu
Donatus Uzodinma Anyanwu
Affiliation:
University of Nigeria, Nsukka
Get access Rights & Permissions [Opens in a new window]

Extract

If a second order ordinary differential equation has a simple or a double pole at a point zfl, then the standard Liouville-Green approximation could sometimes be valid near that point. In this paper we present an asymptotic series solution that is always valid near a double pole. A solution for that of a simple pole is also indicated. Asymptotic validity is proved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 1 , January 1982 , pp. 111 - 118
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Dingle, R. B.The Generalized W.K.B. Method. Appl. Sci. Res. B 5 (1956), 346–367.Google Scholar
(2)Lynn, R. Y. S. and Keller, J. B.Uniform asymptotic solutions of second order linear ordinary differential equations with turning points. Comm. Pure Appl. Math. 23 (1970), 379–408.CrossRefGoogle Scholar
(3)Olver, P. W. J.Asymptotics and Special Functions, London, Academic Press, 1974.Google Scholar