Boundary layers and the method of multiple scales P2, 40 pts. Just some calculations involving boundary layers. Find a composite expansion of the following problems and sketch a solution. You'll probably want to be careful: the location of the boundary layer(s) may not be immediately obvious and could require some playing around. Note: yes, this implies that both ends could possibly have a boundary layer... but the procedure is completely analogous to the case of a single boundary layer. (a) ey" + €(x + 1)²y' - y = x - 1 for 0 < x < 1 where y(0) = 0 and y(1) = −1. (b) ey" — y' + y² = 1 for 0 < x < 1 where y(0) = 1/3 and y(1) = 1.
Boundary layers and the method of multiple scales P2, 40 pts. Just some calculations involving boundary layers. Find a composite expansion of the following problems and sketch a solution. You'll probably want to be careful: the location of the boundary layer(s) may not be immediately obvious and could require some playing around. Note: yes, this implies that both ends could possibly have a boundary layer... but the procedure is completely analogous to the case of a single boundary layer. (a) ey" + €(x + 1)²y' - y = x - 1 for 0 < x < 1 where y(0) = 0 and y(1) = −1. (b) ey" — y' + y² = 1 for 0 < x < 1 where y(0) = 1/3 and y(1) = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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problem (b)
Transcribed Image Text:Boundary layers and the method of multiple scales
P2, 40 pts. Just some calculations involving boundary layers. Find a composite
expansion of the following problems and sketch a solution. You'll probably want to be
careful: the location of the boundary layer(s) may not be immediately obvious and could
require some playing around. Note: yes, this implies that both ends could possibly
have a boundary layer... but the procedure is completely analogous to the case
of a single boundary layer.
(a) ey" + €(x + 1)²y' - y = x - 1 for 0 < x < 1 where y(0) = 0 and y(1) = −1.
(b) ey" — y' + y² = 1 for 0 < x < 1 where y(0) = 1/3 and y(1) = 1.
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