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Why does this blow up?

by rsq_a
Tags: blow
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rsq_a
#1
Feb9-09, 08:33 AM
P: 110
I'm looking at the BVP:

[tex]y'' + ay' + e^{ax}y = 1[/tex],

with y(0) = 0 and y(10) = 0.

The numerical solution blows up at certain values of [tex]a[/tex]. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?
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rsq_a
#2
Feb9-09, 08:44 AM
P: 110
Quote Quote by rsq_a
I'm looking at the BVP:

[tex]y'' + ay' + e^{ax}y = 1[/tex],

with y(0) = 0 and y(10) = 0.

The numerical solution blows up at certain values of [tex]a[/tex]. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?
Erm. I found the problem. Near those values of 'a', there exists a zero eigenvalue of the linear operator. I guess that means that,

[tex]y'' + ay' + e^{ax}y = 0\cdot u^* = 1[/tex],

is a possible solution, and thus the eigenfunction [tex]u^* \to \infty[/tex] will cause the blowup.

Is this correct? It's been a while since I've done Sturm-Liouville stuff.
jacophile
#3
Feb9-09, 07:17 PM
P: 22
What is x?

rsq_a
#4
Feb9-09, 07:18 PM
P: 110
Why does this blow up?

Quote Quote by jacophile View Post
What is x?
[tex]y=y(x)[/tex]


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