
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 secondorder 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 complexvalued and the realvalued 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