Consider the 2-point boundary value problem -u"(x)+2au'(x)=1, (0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Consider the 2-point boundary value problem
-u"(x)+2au'(x)=1, (0<x<1)
(u(0) = u(1) = 0
where a is a positive parameter. Discretize (1) on a uniform grid
0 = x0 < x1 < ... < IN <IN+1 = 1
with N + 1 intervals of length A = xi − xi−1 = 1/(N+1).
-
(a) Verify (algebraically) that the exact solution is given by
u(x) =
1+ (e²a
-
1)x-e2ax
2a(e2a - 1)
0≤x≤1.
Transcribed Image Text:Consider the 2-point boundary value problem -u"(x)+2au'(x)=1, (0<x<1) (u(0) = u(1) = 0 where a is a positive parameter. Discretize (1) on a uniform grid 0 = x0 < x1 < ... < IN <IN+1 = 1 with N + 1 intervals of length A = xi − xi−1 = 1/(N+1). - (a) Verify (algebraically) that the exact solution is given by u(x) = 1+ (e²a - 1)x-e2ax 2a(e2a - 1) 0≤x≤1.
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