Accession Number : AD0283433

Title :   ASYMPTOTIC SOLUTIONS OF A NONHOMOGENEOUS DIFFERENTIAL EQUATION WITH A TURNING POINT

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : CLARK,R.A.

Report Date : JUL 1962

Pagination or Media Count : 1

Abstract : A line r second-order differential equation of the form (1) d2 U/dt2 + 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 S(z) = 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)

Descriptors :   *DIFFERENTIAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE