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Two-Point Boundary Value Problems

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Part of the Texts in Applied Mathematics book series (TAM, volume 50)

Keywords

Boundary Layer Live Load Formal Approximation Matching Relation Regular Expansion 
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5.6 Guide to the Literature

  1. 36.
    de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.Google Scholar
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    de Groen, P.P.N. (1977), Spectral properties of second order singularly perturbed boundary value problems with turning points, J. Math. Anal. Appl. 57, pp. 119–149.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 38.
    de Groen, P.P.N. (1980), The nature of resonance in a singular perturbation problem of turning point type, SIAM J. Math. Anal. 11, pp. 1–22.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 41.
    Dorr, F.W., Parter, S.V., and Shampine, L.F. (1973), Application of the maximum principle to singular perturbation problems, SIAM Rev. 15, pp. 43–88.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 43.
    Eckhaus, W. (1979), Asymptotic Analysis of Singular Perturbations, North-Holland, Amsterdam.zbMATHGoogle Scholar
  6. 45.
    Eckhaus, W. and de Jager, E.M. (1966), Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rat. Mech. Anal. 23, pp. 26–86.zbMATHCrossRefGoogle Scholar
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    Holmes, M.H. (1998), Introduction to Perturbation Methods, Texts in Applied Mathematics 20, Springer-Verlag, New York.Google Scholar
  8. 148.
    O’Malley, Jr., R.E. (1991), Singular Perturbation Methods for Ordinary Differential Equations, Applied Mathematical Sciences 89, Springer-Verlag, New York.Google Scholar
  9. 173.
    Smith, D.R. (1985), Singular Perturbation Theory: An Introduction with Applications, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  10. 186.
    Vainberg, B.R. (1989), Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach, New York.zbMATHGoogle Scholar
  11. 215.
    Ward, M.J. (1992), Eliminating indeterminacy in singularly perturbed boundary value problems with translation invariant potentials, Stud. Appl. Math. 91, pp. 51–93.Google Scholar
  12. 216.
    Ward, M.J. (1999), Exponential asymptotics and convection-diffusion-reaction models, in Proceedings Symposia Applied Mathematics 56, pp. 151–184 (Cronin, J., and O’Malley, Jr., R.E., eds.), American Mathematical Society, Providence, RI.Google Scholar
  13. 217.
    Wasow, W. (1965), Asymptotic Expansions for Ordinary Differential Equations, Interscience, New York.zbMATHGoogle Scholar
  14. 218.
    Wasow, W. (1984), Linear Turning Point Theory, Springer-Verlag, New York.Google Scholar

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© Springer Science+Business Media, Inc. 2005

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