On the Boundary Value Problems for Ordinary Differential Equations with Turning Points

Jiang Fu-ru

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(2): 108-117

Jiang Fu-ru. On the Boundary Value Problems for Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1991, 12(2): 108-117.

Citation:

Jiang Fu-ru. On the Boundary Value Problems for Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1991, 12(2): 108-117.

Citation:

Jiang Fu-ru. On the Boundary Value Problems for Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1991, 12(2): 108-117.

PDF( 526 KB)

On the Boundary Value Problems for Ordinary Differential Equations with Turning Points

Jiang Fu-ru

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

Received Date: 1990-02-24
Publish Date: 1991-02-15

Abstract

Abstract

In this paper, we consider the boundary value problems of the form ey"-f(x,e)y'+g(x,e)y=0(-a≤x≤b,0<ε≤1)y(-a)=a,y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.
- ordinary differential equations,
- singular perturbation,
- turning point problem

FullText(HTML)

References(8)

References

[1]	Wasow,W.,Asymptotic Expansions for Ordinary Differential Equations,Wiley(Interscience),New York(1965).
[2]	Watts,A.M.,A singular perturbation problem with a turning point,Bull.Australian Math.Soc.,5(1971),61-73.
[3]	Ackerberg,R.C.and R.E.O'Malley,Jr.,Boundary layer problems exhibiting resonance,Stud.Appl.Math.,49(1970),277-295.
[4]	O'Malley,R.E.,Jr.,Introduction to Singular Perturbations,Academic Press,New York(1974).
[5]	Matkowskey,B.J.,On boundary layer problems exhibiting resonance.SIAM Rev.,17(1975),82-100.
[6]	江福女,关于常微分方程转点问题共振的必要条件,应用数学和力学,10,4(1989),277-284.
[7]	De Groen,P.P.N.,The singularly perturbed turning point problem:a spectral approach.Singular Perturbation and Asymptotic,Academic Press,New York(1980),149-172.
[8]	Skinner,L.A.,Uniform solution of boundary layer problems exhibiting resonance,SIAM J.Appl.Math.,47,2(1987),225-231.