Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Second-order differential equations with fractional transition points

Author: F. W. J. Olver
Journal: Trans. Amer. Math. Soc. 226 (1977), 227-241
MSC: Primary 34E20
MathSciNet review: 0430445
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An investigation is made of the differential equation

$\displaystyle {d^2}w/d{x^2} = \{ {u^2}{(x - {x_0})^\lambda }f(u,x) + g(u,x)/{(x - {x_0})^2}\} w,$

in which u is a large real (or complex) parameter, $ \lambda $ is a real constant such that $ \lambda > -2$, x is a real (or complex) variable, and $ f(u,x)$ and $ g(u,x)$ are continuous (or analytic) functions of x in a real interval (or complex domain) containing $ {x_0}$. The interval (or domain) need not be bounded. Previous results of Langer and Riekstins giving approximate solutions in terms of Bessel functions of order $ 1/(\lambda + 2)$ are extended and error bounds supplied.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34E20

Retrieve articles in all journals with MSC: 34E20

Additional Information

Keywords: Asymptotic analysis, Bessel functions, error analysis, linear differential equations, transition point, turning point
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society