On the Asymptotic Solutions for a Class of Second Order Differential Equations with Slowly Varying Coefficients

Qiao Zong-chun

Volume 12 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(7): 653-660

Qiao Zong-chun. On the Asymptotic Solutions for a Class of Second Order Differential Equations with Slowly Varying Coefficients[J]. Applied Mathematics and Mechanics, 1991, 12(7): 653-660.

Citation:

Qiao Zong-chun. On the Asymptotic Solutions for a Class of Second Order Differential Equations with Slowly Varying Coefficients[J]. Applied Mathematics and Mechanics, 1991, 12(7): 653-660.

Citation:

Qiao Zong-chun. On the Asymptotic Solutions for a Class of Second Order Differential Equations with Slowly Varying Coefficients[J]. Applied Mathematics and Mechanics, 1991, 12(7): 653-660.

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On the Asymptotic Solutions for a Class of Second Order Differential Equations with Slowly Varying Coefficients

Qiao Zong-chun

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Universitg of Technology, Shanghai

Received Date: 1989-11-23
Publish Date: 1991-07-15

Abstract

Abstract

In this paper we study the asymptotic expansions of the solutions for a class of second order ordinary differential equations with slowly varying coefficients. The defect of the known works on these problems is noted, and the results in [1-4],[5-7] are improved and extended by means of the modified method of multiple scales^[8].
- ordinary differential equations,
- slowly varying coefficient,
- asymptotic expansion solution

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References(8)

References

[1]	Feshchenko,S.F.,N.I.Shkio’and L.D.NIkolenko,Asymptotic Method in the Theory of Linear Differential Equations,American Elsevier,New York,(1967).
[2]	Fowler,R.H.,E.G.Gaup,C.N.H.Lock,and H.W.Richmond,The Aerodynamics of a Spinning Shell,Phil.Trans.Roy.Soc.London,221,(1973).
[3]	Fowler,R.H.,and C.H.N.Lock,Approximate Solutions of Linear Differential Equations,Proc.London Math.Soc.20(1921).
[4]	Nayfeh,A.H.,Perturbation Methods,Wiley(1973).
[5]	Kevorkian,J.,and Cole,J.D.,Perturbation Methods in Applied Mathematics,Spring-Verlag,(1981).
[6]	Kevorkian,J.,Passage through Reasonance for a One-dimensional Oscillator with Slowly Varying Frequency,SIAM J.on Appl.Math.,20,(1971).
[7]	江福汝、徐传基、徐宝智,织机梭子的运动方程及其渐近解,振动与冲击1(13)(1985).
[8]	Jiang Fu-ru,On Boundary Layer Methods,Appl.Math,and Mech.,2,5(1981).

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