Article citationsMore>>

Fraenkel, L.E. (1969) On the Method of Matched Asymptotic Expansions. Mathematical Proceedings of the Cambridge Philosophical Society, 65, 263-284.
https://doi.org/10.1017/S0305004100044236

has been cited by the following article:

• TITLE: Simple Singular Perturbation Problems with Turning Points

  AUTHORS: Na Wang

  KEYWORDS: Singular Perturbations, Asymptotic Methods, Boundary Value Problems, Turning Points, Boundary and Interior Layers, Boundary Layer Resonance

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.12, December 9, 2019

  ABSTRACT: The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 ≪1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.