A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point

Zhang Ju-ling

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Zhang Ju-ling. A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point[J]. Applied Mathematics and Mechanics, 1994, 15(1): 77-86.

Citation:

Zhang Ju-ling. A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point[J]. Applied Mathematics and Mechanics, 1994, 15(1): 77-86.

Citation:

Zhang Ju-ling. A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point[J]. Applied Mathematics and Mechanics, 1994, 15(1): 77-86.

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A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point

Zhang Ju-ling

Sichuan Institute of Light Industry and Chemical Technology, Zigong

Received Date: 1992-06-01
Publish Date: 1994-01-15

Abstract

Abstract

A second order linear ordinary differential equation has been studied,and the complete expression.of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended airy function.
- uniformly valid,
- asymptotic solution,
- turning point

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References(5)

References

[1]	张居铃,广义Airy函数与具有n个转向点的方程,应用数学和力学,12(9)(1991).
[2]	Nayfeh,A.H.Pertubation Methods,(1973).
[3]	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),103-12s.
[4]	Moriguchi,H.,An improvement of the WKB method in the presence of turning points and the asymptotic solutions of 2 class of Hill equation,J.Phy.Soc.Japan,14 (1959),1711-1796.
[5]	Lynn,R.Y.and J.B.Keller,Uniform asymptotic solutions of second order lineardifferential equations with turning points,Comm.Pure Appl.Math.,(1970),23,379-408.