Abstract
A second order linear ordinary differential equation has been studied, and the complete expresson, of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended Airy function.
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Zhang Ju-ling, Extended Airy Function and Diferential Equations withn-Turning Points,Appl. Math. and Mech.,12, 9 (1991), 907–926.
A. H. Nayfeh,Pertubation Methods, (1973).
Mckelvey, R. W., The solutions of second order linear ordinary differential equations about a turning point of order two, Trans.Am. Math. Soc., 79 (1959), 103–123.
Moriguchi, H., An improvement of the WKB method in the presence of turning points and the asvmptotic solutions of 2 class of Hill equation,J. Phy. Soc. Japan, 14 (1959), 1711–1796.
Lynn, R. Y. and J. B. Keller, Uniform asymptotic solutions of second order linear differential equations with turning points,Comm. Pure Appl. Math., (1970), 23, 379–408.
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communicated by Ding Xie-ping
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Ju-ling, Z. A complete expression of the asymptotic solution of differential equation with n-th order turning point. Appl Math Mech 15, 81–91 (1994). https://doi.org/10.1007/BF02451030
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DOI: https://doi.org/10.1007/BF02451030