On an internal boundary layer problem

Authors:
R. Wong;Heping Yang
Affiliations:
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China;Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
Venue:
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Year:
2002

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Abstract

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 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.