Why does this blow up?

  1. 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?
     
  2. jcsd
  3. 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.
     
  4. What is x?
     
  5. [tex]y=y(x)[/tex]
     
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