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Boundary layer methods for ordinary differential equations with small coefficients multiplying the highest derivatives

Part of the Lecture Notes in Mathematics book series (LNM,volume 430)

Abstract

Many singular perturbation problems of applied mathematics involve differential equations with a small parameter multiplying the highest derivatives. Many of the asymptotic results obtained through the familiar boundary layer methods carry over to equations with small coefficients multiplying these derivatives. Moreover, these results can be readily obtained through numerical experimentation. Specific results are given for boundary value problems for certain higher order linear equations and for some second order quasilinear equations.

Keywords

  • Asymptotic Solution
  • Small Coefficient
  • Singular Perturba
  • Singular Perturbation Problem
  • Full Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work supported in part by the Office of Naval Research under Grant No. N00014-67-A-0209-0022.

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© 1974 Springer-Verlag

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O'Malley, R.E. (1974). Boundary layer methods for ordinary differential equations with small coefficients multiplying the highest derivatives. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066277

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  • DOI: https://doi.org/10.1007/BFb0066277

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  • Print ISBN: 978-3-540-07021-4

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