Advertisement

Applied Mathematics and Mechanics

, Volume 22, Issue 3, pp 282–293 | Cite as

On the asymptotic solutions of boundary value problems for a class of systems of nonlinear differential equations (I)

  • Jiang Fu-ru
Paper of Special Issue of Appl Math Mech on 20th Anniversary
  • 16 Downloads

Abstract

A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u″=v, εv″+f(x, u, u′)v′−g(x, u, u′)v=0 (0<ε≪1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.

Key words

system of nonlinear differential equations boundary value problems asymptotic solution 

CLC number

O302 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Dorr F W, Parter S V. Singular perturbations of nonlinear boundary value problems with turning points[J].J Math Anal Appl, 1970,29:273–293.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Dorr F W, Parter S V. Shampine L F. Applications of the maximum principle to singular perturbation problems[J].SIAM Rev, 1973,15:43–88.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Howes F A, Shao S. Asymptotic analysis of model problems for a coupled systems[J].Nonlinear Anal, 1989,13(9):1013–1024.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Harris W A, Shao S. Refined approximations of the solutions of a coupled system with turning points[J].J Differential Equations, 1991,92:125–144.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    JIANG Fu-ru. On the boundary layer method[J].Applied Mathematics and Mechanics (English Edition), 1981,2(5):505–518.MathSciNetCrossRefGoogle Scholar
  6. [6]
    JIANG Fu-ru. On the singular perturbations of nonlinear boundary value problems for ordinary differential equations[J].Scientia Sinica, 1987,30(6):588–600.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Jiang Fu-ru
    • 1
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP R China

Personalised recommendations