On an internal boundary layer problem
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Related Research Unit(s)
|Journal / Publication||Journal of Computational and Applied Mathematics|
|Publication status||Published - 1 Jul 2002|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-0036644483&origin=recordpage|
In this paper, we consider the boundary value problem εy″+ a(x)y′ + b(x)y = 0, x ∈ [x-,x+], x- <0 <x+, y(x-) = A, y(x+) = B, where A and B are two prescribed constants, and 0 <ε ≪ 1 is a small positive parameter. As x → 0, it is assumed that a(x) ~ αx and b(x) ~ β, where α > 0 and β/α ≠ 1,2,3,... . Under certain smoothness conditions on a(x) and b(x), an asymptotic solution is constructed, which holds uniformly for x ∈ [x-,x+]. This result is proved rigorously by using the method of successive approximation. © 2002 Elsevier Science B.V. All rights reserved.