Author(s)

Na Wang

Department of Applied Mathematics, Shanghai Institute of Technology, Shanghai, China.

The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 < ε ≪ 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.

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

Wang, N. (2019) Simple Singular Perturbation Problems with Turning Points. Journal of Applied Mathematics and Physics, 7, 2979-2989. doi: 10.4236/jamp.2019.712208.