Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T10:38:14.695Z Has data issue: false hasContentIssue false
  • English
  • Français

A singular perturbation problem with a turning point

Published online by Cambridge University Press:  17 April 2009

A.M. Watts
A.M. Watts
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the equation

εy″ + p(x)y′ + q(x)y = 0, where ε is a small positive parameter and p vanishes in the interval. Two asymptotic forms of solution are obtained and a rigorous estimate is made of the difference between the exact solutions and the asymptotic forms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 1 , August 1971 , pp. 61 - 73
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Ackerberg, R.C. and O'Malley, R.E. Jr, “Boundary layer problems exhibiting resonance”, Studies in Appl. Math. 49 (1970), 277–295.CrossRefGoogle Scholar
[2]Erdélyi, A., “On a nonlinear boundary value problem involving a small parameter”, J. Austral. Math. Soc. 2 (1961/1962), 425–1439.CrossRefGoogle Scholar
[3]Miller, J.C.P., “Parabolic cylinder functions”, Handbook of mathematical functions with formulas, graphs and mathematical tables, 685–720 (edited by Abramowitz, Milton; Stegun, Irene A., National Bureau of Standards Applied Mathematics Series 55; United States Department of Commerce, 1964; reprinted, Dover, New York, 1965).Google Scholar
[4]Mitropol'skii, Yu. A., Problems of the asymptotic theory of nonstationary vibrations (translated from the Russian by Gutfreund, Ch.; Israel Program for Scientific Translations, Jerusalem, 1965).Google Scholar