Accession Number:

AD0283433

Title:

ASYMPTOTIC SOLUTIONS OF A NONHOMOGENEOUS DIFFERENTIAL EQUATION WITH A TURNING POINT

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1962-07-01

Pagination or Media Count:

1.0

Abstract:

A line r second-order differential equation of the form 1 d2 Udt2 2 t t, U 2 t, is considered with the real variable t ranging over a finite closed interval. The parameter is assumed to be large and complex-valued and the real-valued function is assumed to have a single zero of first order, known as a tuning point. Assuming that and are analytic in for 0 0 and that , , and are infintely differentiable in t , two types of formal solutions are constructed in terms of a solution of the differential equation 2 S z z Sz 1 . Properties of solutions of 2 are established and it is shown that, when lies in a given quadrant of the -plane, S can be chosen so that the formal solutions funish asymptotic representations of actual solutions of 1 provided is sufficiently large. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE