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Zbl 0809.34071
Skinner, L.A.
Matched expansion solutions of the first-order turning point problem. (English)
[J] SIAM J. Math. Anal. 25, No.5, 1402-1411 (1994). ISSN 0036-1410; ISSN 1095-7154/e

Author's abstract: ``Uniformly valid asymptotic solutions for second- order linear differential equations with first-order turning points are obtained by the method of matched asymptotic expansions. A key feature of the analysis is that the high frequency and strong exponential behavior of these solutions is factored out of the matching processes. This produces a set of essentially elementary boundary layer problems. A variation of the Langer expansion theorem for the first-order turning points is independently established and used in verifying the formal calculations. The results emphasize the basic WKB structure of turning points asymptotics. A new property of Airy functions is also involved''.
[J.Mika (Durban)]

MSC 2000:: *34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: asymptotic solutions; second-order linear differential equations with first-order turning points; method of matched asymptotic expansions; boundary layer problems; Langer expansion theorem; WKB structure; Airy functions

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