TY - JOUR
T1 - On an internal boundary layer problem
AU - Wong, R.
AU - Yang, Heping
PY - 2002/7/1
Y1 - 2002/7/1
N2 - In this paper, we consider the boundary value problem εy″+ a(x)y′ + b(x)y = 0, x ∈ [x-,x+], x- <0 +, 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.
AB - In this paper, we consider the boundary value problem εy″+ a(x)y′ + b(x)y = 0, x ∈ [x-,x+], x- <0 +, 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.
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U2 - 10.1016/S0377-0427(01)00569-6
DO - 10.1016/S0377-0427(01)00569-6
M3 - 21_Publication in refereed journal
VL - 144
SP - 301
EP - 323
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1-2
ER -