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Matched expansion solutions of the first-order turning point problem. (English) Zbl 0809.34071
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”.
Reviewer: J.Mika (Durban)
MSC:
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)